cuboidal UCDavisOrganology TermsCells&Tissues epithelial epitypes epitypes2 Types of Epithelium ...Expert subject Molecular and Cellular Biology date February 2009 Infobox Anatomy Name Simple cuboidalepithelium Latin GraySubject GrayPage Image Gray1133.png Caption Transverse section of pyramidal substance of kidney of pig, the blood vessels of which are injected br a. Large collecting tube, cut across, lined with cylindrical epithelium br b. Branch of collecting tube, cut across, lined with cubical epithelium br c, d. Henle s loops cut across br e. Blood vessels cut across. br D. Connective tissue ground substance. Image2 Caption2 System MeshName MeshNumber DorlandsPre DorlandsSuf Code TerminologiaHistologica 2 00 02.0.02019 Simple cuboidal epithelia are epithelium epithelial cells in a single layer of cubelike cells with large, spherical central nuclei. Simple cuboidal epithelia are found on the surface of Ovary ovaries , the lining of nephron s, the walls of the renal tubule s, and parts of the human eye eye and thyroid . On these surfaces, the cells perform secretion and absorption. Function These cells provide protection and may be active pumping material in or out of the lumen or passive, depending on the location and cellular specialization. They are also found in kidney tubules, glandular ducts, ovaries, and the thyroid gland. Simple cuboidal cells are found in single rows with their spherical nuclei in the center of the cells and are directly attached to the Basal lamina basal surface . They also constitute the germinal epithelium which produces the egg cells in the female ovary and the sperm cells in the male testes. ref http www.bcb.uwc.ac.za Sci Ed grade10 mammal epithelial.htm Epithelial Tissues. Department of Biodiversity & Conservation Biology, University of the Western Cape. ref These cells offer some protection and function in absorption and secretion. Additional images gallery Image Illu epithelium.jpg Types of epithelium Image Gray1176.png Section ... more details
them drying out and dying. Types of non keratinised stratified squamous epithelium include cornea see also corneal epithelium , oral cavity , esophagus , anal canal , vagina , and the internal ... granulosum. Types of keratinized stratified squamous epithelium include skin , tongue filiform papillae ... Illu epithelium.jpg Epithelium Image Barretts alcian blue.jpg Micrograph of normal stratified squamous epithelium right of image and the metaplasia metaplasic epithelium of Barrett s esophagus left of image ... more details
Infobox Anatomy Name PAGENAME Latin GraySubject GrayPage Image Illu epithelium.jpg Caption Types of epithelium Image2 Caption2 Precursor System Artery Vein Nerve Lymph MeshName MeshNumber Code TerminologiaHistologica 2 00 02.0.02032 Stratified columnar epithelia is a rare type of epithelial tissue composed of column shaped cells arranged in multiple layers. Stratified columnar epithelia are found in the ocular conjunctiva of the human eye eye , in parts of the pharynx and anus , the female s uterus , the male urethra and vas deferens . Also found in intralobular ducts in salivary glands . The cells function in secretion and protection . References reflist External links http www.cytochemistry.net microanatomy epithelia stratified columnar.htm Stratified columnar epithelium at cytochemistry.net AnatomyAtlasesMicroscopic 02 23 Stratified Columnar Epithelium anatomy stub Epithelial types Category Epithelial cells pt Epit lio colunar estratificado ... more details
Stratified epithelial lining can refer to Stratified squamous epitheliumStratified columnar epitheliumStratifiedcuboidalepithelium disambig ... more details
thick, it is known as stratifiedepithelium . ref name vanLommel 2002 p97 van Lommel, 2002 http books.google.com ... at different heights, they can be confused with stratified epithelia. This kind of epithelium ..., bronchi e.t.c. Table of simple epithelium types StratifiedepitheliumStratifiedepithelium differs ... layers the cells can be squamous, cuboidal or columnar. citation needed date January 2011 Stratified ... vanLommel 2002 p97 Stratified epithelia of columnar, cuboidal or squamous type can have the following ... of a non keratinized or moist stratifiedepithelium. citation needed date January 2011 ... appear to be stratifiedcuboidal when the tissue is not stretched or stratified squamous when the organ ... lumen of bodies. The outermost layer of our skin is composed of dead Squamous epitheliumstratified ... skin nonkeratinized stratified squamous epithelium. Other surfaces that separate body cavities from ... Nonkeratinized stratified squamous epithelium 500x gallery See also Wiktionary Blastula Gastrulation ...About the epithelium as it relates to animal anatomy the fungal structure of the same name Pileipellis Infobox Anatomy Name Epithelium Latin GraySubject GrayPage Image Tkanka nablonkowa.png a deleted image Caption Epithelium Image2 Caption2 Precursor System Artery Vein Nerve Lymph MeshName MeshNumber Code TerminologiaHistologica 2 00 02.0.00001 Epithelium is one of the four basic types of animal Tissue ... nipple . ref http en.wiktionary.org wiki epithelium Epitheium at Wiktionary ref Epithelial layers ... are highly vascular. General structure Cells in epithelium are very densely packed together like bricks ... cells rest on a basement membrane , which acts as a scaffolding on which epithelium can grow ... will be able to enter the epithelium. ref name Eurell 2006 p18 cite book editors Eurell, Jo Ann ... thumb 350px Types of epithelium Tissues are generally classified by the morphology of their cells ...&pg PA8 ref Epithelial tissue that is only one cell thick is known as simple epithelium . ref van ... more details
Infobox Anatomy Name PAGENAME Latin GraySubject GrayPage Image Illu epithelium.png Caption Epithelium Image2 Caption2 Precursor System Artery Vein Nerve Lymph MeshName MeshNumber Code TerminologiaHistologica 2 00 02.0.01013 Cuboidal epithelia are epithelial cell biology cells having a cube like shape that is, their width is approximately equal to their height. They may exist in single layers simple cuboidalepithelium or multiple layers stratifiedcuboidalepithelium depending on their location and thus function in the body. anatomy stub Epithelial types Category Epithelial cells pt Epit lio c bico ... more details
EpitheliumCuboidalcuboidal cells thought to have some ability to differentiate into other cells types found within the epithelium. For example, these basal cells respond to injury of the airway epithelium ... of the respiratory epithelium in these areas, it changes to stratified squamous epithelium , which ... epithelium beat in concert cranially, effectively moving secreted mucus containing trapped ... more details
Infobox Anatomy Name PAGENAME Latin GraySubject GrayPage Image Harnblase Urothel.png Caption Transitional epithelium of the urinary bladder . Note the rounded surface of the apical cells a distinguishing characteristic of this type of epithelium. Image2 Gray1134.png Caption2 Transverse section of ureter . System MeshName MeshNumber DorlandsPre e 13 DorlandsSuf 12339236 Code TerminologiaHistologica 2 00 02.0.02033 Transitional epithelium also known as urothelium is a type of tissue consisting of multiple layers of epithelial cells which can contract and expand. These cells, part of the epithelium , are found in the urinary bladder , in the ureters , and in the superior urethra and gland ducts of the prostate . Appearance These cells appear to be cuboidal with a domed apex when the organ or the tube in which they reside is not stretched. When the bladder fills, the tissue actually compresses and the cells become stretched, and they appear to be flat, irregular, and squamous . Functions The transitional epithelium cells accommodate fluctuation of volume of the liquid in an organ or tube, such as the urinary bladder, and protect against the caustic effects of urine . Surfaces The free surface of the tissue the part that faces outward into the organ or tube is called the apical surface or free surface. The part that lines the bottom of the tissue is called the basement membrane . See also Urothelium Additional images gallery Image Illu epithelium.jpg Types of epithelium Image Illu transitional epithelium.svg Schematic view of transitional epithelium Image Gray1141.png Vertical section of bladder wall. gallery External links http cellbio.utmb.edu microanatomy epithelia transitional epithelium.htm Histology at utmb.edu OklahomaHistology 36 02 ureter OklahomaHistology 37 02 urinary bladder AnatomyAtlasesMicroscopic 02 24 Transitional Epithelium , Ureter KansasHistology urinary renal16 ureter cell biology stub Epithelial types Category Epithelial cells cs P echodn epitel et ... more details
Image The Periodontium.jpg 280px thumb right The gingiva gingival sulcus G is bounded by the Tooth enamel enamel of the crown tooth crown A of the tooth and the sulcular epithelium . Immediately Commonly used terms of relationship and comparison in dentistry apical to the base of the pocket, and Commonly used terms of relationship and comparison in dentistry coronal to the most coronal of the gingival fibers H is the junctional epithelium . The junctional epithelium is that epithelium which lies at, and in health also defines, the base of the gingiva gingival sulcus . It attaches to the surface of the tooth with hemidesmosome s and is, on average, roughly 1 mm in width in the Commonly used terms of relationship and comparison in dentistry apico coronal dimension, constituting about one half of the biologic width . ref Carranza s Clinical Periodontology, 9th Ed. W.B. Saunders, 2002, page 23. ref The junctional epithelium, a keratinized non keratinized stratified squamous epithelium , ref AAP 2010 In Service Exam, question A 20 ref lies immediately Commonly used terms of relationship and comparison in dentistry apical to the sulcular epithelium , which lines the gingival sulcus from the base to the free gingival margin , where it interfaces with the epithelium of the oral cavity. Cell biology Cells in the junctional epithelium tend to have wide inter cellular spaces, to allow the transmission of white blood cell s from blood vessel s to the bottom of the gingival sulcus, to help prevent disease. Damage to the junctional epithelium results in it being irregular in texture, rather than smooth, and the formation of pocket epithelium, which is a histopathological characteristic of gum disease . References references Periodontology Category Gingiva Gray s ... more details
In statistics , stratified sampling is a method of sampling statistics sampling from a Population statistics population . In statistical survey s, when subpopulations within an overall population vary, it is advantageous to sample each subpopulation stratum independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should be mutually exclusive every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive no population element can be excluded. Then simple random sampling or systematic sampling is applied within each stratum. This often improves the representativeness of the sample by reducing sampling error. It can produce a weighted mean that has less variability ... , stratified sampling is a method of variance reduction when Monte Carlo method s are used to estimate population statistics from a known population. Stratified sampling strategies Proportionate ... stratified sampling would be for a political Statistical survey survey . If the respondents needed ... population as mentioned above. A stratified survey could thus claim to be more representative of the population ... density varies greatly within a region, stratified sampling will ensure that estimates can be made ... can also be used to improve population representativeness in a study. Disadvantages Stratified sampling ... subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling ... to be stratified by variance, there is no way to make the subgroup sample sizes proportional at the same ... are asked to take a sample of 40 staff, stratified according to the above categories. The first step ... Portal Statistics Opinion poll Opinion Poll Statistical benchmarking Sample size Stratified sample size Stratified sample size References references Statistics collection state collapsed DEFAULTSORT Stratified Sampling Category Sampling statistics Category Sampling techniques Category Statistical terminology ... more details
in PRK or other non flap vision correction procedures. See also Stratified squamous epithelium ...Infobox Anatomy Name Corneal epithelium Latin e. anterius corneae GraySubject 225 GrayPage 1007 Image Gray871.png Caption Vertical section of human cornea from near the margin. Waldeyer. Magnified. BR 1. Epithelium. BR 2. Bowman s membrane Anterior elastic lamina . BR 3. substantia propria . BR 4. Descemet s membrane Posterior elastic lamina . BR 5. corneal endothelium Endothelium of the anterior chamber . BR a. Oblique fibers in the anterior layer of the substantia propria . BR b. Lamell the fibers of which are cut across, producing a dotted appearance. BR c. Corneal corpuscles appearing wikt fusiform fusiform in section. BR d. Lamell the fibers of which are cut longitudinally. BR e. Transition to the sclera , with more distinct fibrillation, and surmounted by a thicker epithelium . BR f. Small blood vessels cut across near the margin of the cornea . Image2 Caption2 System Precursor MeshName Epithelium, corneal MeshNumber A09.371.060.217.325 DorlandsPre e 13 DorlandsSuf 12339086 The corneal epitheliumepithelium corne anterior layer is made up of epithelial tissue and covers the front of the cornea . It acts as a barrier to protect the cornea, resisting the free flow of fluids from the tears, and prevents bacteria from entering the epithelium and corneal stroma. The corneal epithelium consists of several layers of cells. The cells of the deepest layer are Simple columnar epithelium columnar , known as basal cells. Then follow two or three layers of polyhedral cells, commonly known as wing cells. The majority of these are prickle cell s, similar to those found in the stratum ... cell nucleus nuclei . The layers of the epithelium are constantly undergoing mitosis. Basal and wing ... corneaingrowth.html Epithelium Ingrowth After LASIK Eye Epithelial types DEFAULTSORT Corneal Epithelium Category Eye anatomy es Epitelio corneal pt Corneal epithelium ru ... more details
Orphan date September 2008 Coelomic epithelium refers to the epithelium that lines the surface of the body wall and abdomen abdominal organs. It constitutes the outermost layer of the male and female gonad s, thus forming the Germinal epithelium female germinal epithelium of the female or Germinal epithelium male of the male . It is also called the germinal epithelium of Waldeyer or sometimes the superficial epithelial cells in embryology . It is often encountered in the medical setting as an important source of various types of ovarian cancer , primary peritoneal serous cancer and endometriosis coelomic metaplasia . Category Abdomen medicine stub ... more details
Germinal epithelium can refer to Germinal epithelium female , a layer of cells covering the ovary Germinal epithelium male , a layer of cells covering the testicle Germ layer , primary tissue layer formed during embryogenesis in animals See also Germinal disambiguation Epithelium disambig Long comment to avoid being listed on short pages ... more details
Image The Periodontium.jpg 280px thumb right The gingival sulcus G is bounded by the Tooth enamel enamel of the crown tooth crown A of the tooth and the sulcular epithelium . The sulcular epithelium is that epithelium which exists on the sulcular side of the free gingival margin F . The oral epithelium E exists on the other side of the free gingival margin. The sulcular epithelium is that epithelium which lines the gingival sulcus . ref name Carranza s Clinical Periodontology 2002, page 23 Carranza s Clinical Periodontology, W.B. Saunders, 2002, page 23. ref It is Commonly used terms of relationship and comparison in dentistry apically bounded by the junctional epithelium and meets the epithelium of the oral cavity at the height of the free gingival margin . The sulcular epithelium is keratinized nonkeratinized . ref name Carranza s Clinical Periodontology 2002, page 23 References references Periodontology Category Dental anatomy dentistry stub ... more details
Infobox Anatomy Name Olfactory epithelium Latin GraySubject 223 GrayPage 996 Image Gray857.png Caption Section of the olfactory mucous membrane. Image2 Gray772.png Caption2 Plan of olfactory neurons. System MeshName Olfactory Mucosa MeshNumber A04.531.520.573 Code TerminologiaHistologica 3 11 07.0.01001 The olfactory epithelium is a specialized epithelium epithelial tissue inside the nasal cavity that is involved in olfaction smell . In humans, it measures about 1 square centimetre on each side and lies on the roof of the nasal cavity about 7 cm above and behind the nostrils. ref Citation pmid 7143026 publication date 1982 year 1982 last Moran first David T. title The fine structure of the olfactory mucosa in man volume 11 pages 721 746 journal Journal of Neurocytology doi 10.1007 BF01153516 ... epithelium is the part of the olfactory system directly responsible for detecting odor s. Layers of olfactory epithelium Olfactory epithelium consists of four distinct cell types ref Ross, MH, Histology ... of the epithelium are bipolar neurons which congregate to form the olfactory nerve . The olfactory ... glial cells, the supporting cells a.k.a. Sustentacular cell s of the olfactory epithelium function ... on the basal lamina of the olfactory epithelium, basal cells are stem cells capable of division ... leads to the olfactory epithelium being replaced every 2 4 weeks. Basal cells can be divided on the basis ... which line the olfactory epithelium and the slightly more superficial globose basal cells. ref Citation ... washed away. ref name Ross Pathology The olfactory epithelium can be damaged by inhalation of toxic .... Because of its regenerative capacity, damage to the olfactory epithelium can be temporary but in extreme ... varken olfactory epithelium pig.jpg olfactory epithelium pig gallery References Reflist added ... sackler cmdb olfactory.htm Diagram of Olfactory Epithelium Tufts Sackler Olfactory system Epithelial types Commons category Olfactory epithelium DEFAULTSORT Olfactory Epithelium Category Olfactory ... more details
Image Simple columnar epithelium.jpg thumb right 200px Simple columnar epithelium . The intestinal epithelium is the epithelium that covers the small intestine small and large intestine . It is simple columnar and Cilia nonciliated . They primarily take part in the digestive system . However, they also express TLR 4 receptors, ref name Immunology17 Lippincott s Illustrated Reviews Immunology. Paperback 384 pages. Publisher Lippincott Williams & Wilkins July 1, 2007 . Language English. ISBN 0781795435. ISBN 978 0781795432. Page 17 ref and are thus a part of the immune system , both as a barrier and as a first line pathogen recognition system. The mammalian intestine is covered by a single layer of epithelial cells that is renewed every 4 5 days. ref name vanderFlier cite journal unused data first Hans last van der Flier first Laurens G. url http arjournals.annualreviews.org doi abs 10.1146 annurev.physiol.010908.163145 title Stem Cells, Self Renewal, and Differentiation in the Intestinal Epithelium work Annual Review of Physiology volume 71 issue 1 page 241 260 doi 10.1146 annurev.physiol.010908.163145 pmid 18808327 year 2009 last2 Clevers first2 H journal Annual review of physiology ref Epithelial cells in the small intestine are a type of Brush border brush border cell that are joined together by tight junction s to form a polymer impermeable membrane. These cells have a brush border surface to increase their absorptive surface area, thus making them more efficient. Genes important for the formation of intestinal epithelium are listed in Intestinal epithelial differentiation genes this table . References reflist Category Epithelial cells digestive stub fr pith lium intestinal hu B lh m ... more details
The reduced enamel epithelium , sometimes called reduced dental epithelium , overlies a tooth development developing tooth and is formed by two layers a layer of ameloblast cell biology cells and the adjacent layer of cuboidal cells outer enamel epithelium from the dental lamina . As the cells of the reduced enamel epithelium degenerate, the tooth is revealed progressively with its eruption into the mouth . The degeneration of reduced enamel epithelium also mediates the initial epithelium epithelial attachment to the tooth. The Reduced Enamel Epithelium REE consist of Inner Enamel Epithelium Outer Enamel Epithelium References Cate, A.R. Ten. Oral Histology development, structure, and function. 5th ed. 1998. ISBN 0 8151 2952 1. Brand, Richard Isselhard, Donald. Anatomy of Orofacial Structures Anatomy of Orofacial Structures. Mosby. 7 edition March 4, 2003 . ISBN 0323019544 Category Parts of tooth dentistry stub ... more details
Infobox Anatomy Name PAGENAME Latin GraySubject GrayPage Image Germinal epithelium testicle.svg Caption Germinal epithelium of the testicle . 1 basal lamina , 2 spermatogonia , 3 spermatocyte 1st order, 4 spermatocyte 2nd order, 5 spermatid , 6 mature spermatid, 7 Sertoli cell , 8 tight junction blood testis barrier Image2 Caption2 Precursor System Artery Vein Nerve Lymph MeshName MeshNumber DorlandsPre e 13 DorlandsSuf 12339107 The germinal epithelium is the innermost layer of the testicle . Germinal epithelium is also known as the wall of the seminiferous tubule within the testes. It is cells in the epithelium are connected via tight junctions. External links BUHistology 17803loa Male Reproductive System testis, germinal epithelium AnatomyAtlasesMicroscopic 02 21 Stratified Germinal Epithelium EmbryologySwiss cgametogen spermato02 Gray s genitourinary stub Category Male reproductive system Male reproductive system ... more details
Infobox Anatomy Name Germinal epithelium female Latin GraySubject GrayPage Image Ovaire 1.JPG Caption Diagram in French. pith lium ovarien labeled at upper right. Image2 Gray1163.png Caption2 Section of the ovary. 1. Germinal epithelium . 2. Central stroma. 3. Peripheral stroma. 4. Bloodvessels. 5. Vesicular follicles in their earliest stage. 6, 7, 8. More advanced follicles. 9. An almost mature follicle. 9 . Follicle from which the ovum has escaped. 10. Corpus luteum. Precursor System Artery Vein Nerve Lymph MeshName MeshNumber DorlandsPre e 13 DorlandsSuf 12339107 The surface of the ovary is covered by a layer of Simple cuboidalepithelium simple cuboidal cells which constitutes the germinal epithelium of Waldeyer. ref cite journal author Nishida T, Nishida N title Reinstatement of germinal epithelium of the ovary journal Reprod Biol Endocrinol. volume 4 issue pages 42 year 2006 pmid 16923182 pmc 1560142 doi 10.1186 1477 7827 4 42 ref These cells are derived from the mesoderm during embryonic development and are closely related to the mesothelium of the peritoneum . The germinal epithelium gives the ovary a dull gray color as compared with the shining smoothness of the peritoneum and the transition between the mesothelium of the peritoneum and the columnar cells which cover the ovary is usually marked by a line around the anterior border of the ovary. The germinal epithelium is a misnomer and does not give rise to primary follicles. It is known to give rise to ovarian tumors. References reflist External links BUHistology 18403loa OklahomaHistology 83 07 Gray s Female reproductive system DEFAULTSORT Germinal Epithelium Female Category Female reproductive system genitourinary stub cs Z rode n epitel it Epitelio germinale sk Z rodo n epitel ... more details
Unreferenced date March 2009 main iris anatomy The iris pigment epithelium IPE is a two cell thick layer of cuboidal cells lying behind the iris anatomy iris . Both layers are jet black due to the numerous large melanosome s which pack the cytoplasm of each cell. Towards the central axis, the IPE terminates at the pupillary margin. Peripherally, the IPE is continuous with the ciliary epithelium , also double layered but pigmented in only one layer. The ciliary epithelium is continuous in its turn with the multilayered retina , which has an outermost pigmented layer, the retinal pigment epithelium RPE . Despite their very different functions and histological appearances, these regions have a common origin from the two layers of the embryological optic cup embryological optic cup . The melanosomes of the IPE are distinctive, being larger, blacker and rounder than those in the ciliary epithelium or RPE. Iris pigment epithelium is the scientific name for the color of an iris in the eye. Pathology The IPE is affected by glaucoma , diabetes , and iris inflammations and atrophies of various kinds, generally responding by showing patchy thinning and depigmentation. In albinism, it is fully or partially nonpigmented and translucent, which contributes to the photophobia of that condition. However, diseases specific to the IPE itself are almost non existent, and it seems to be a highly differentiated, stable cell type that almost never gives rise to malignancies, unlike the melanocytes of the iris stroma. Reports of adenomas and adenocarcinomas of the IPE exist, but some of these are debatable. eye stub Category eye anatomy ... more details
Infobox embryology Name PAGENAME Latin epithelium enameleum externum GraySubject GrayPage Image Cervical loop.png Caption The cervical loop area 1 dental follicle cells, 2 dental mesenchyme, 3 Odontoblasts, 4 Dentin, 5 stellate reticulum, 6 outer enamel epithelium, 7 inner enamel epithelium, 8 ameloblasts, 9 enamel. Image2 Caption2 MeshName MeshNumber Code TerminologiaEmbryologica 05 04 .1.1.2.3.12 The outer enamel epithelium , also known as the external enamel epithelium , is a layer of cuboidal cell biology cells located on the periphery of the enamel organ in a tooth development developing tooth . This layer is first seen during the bell stage. The rim of the enamel organ where the outer and inner enamel epithelium join is called the cervical loop . References Cate, A.R. Ten. Oral Histology development, structure, and function. 5th ed. 1998. ISBN 0 8151 2952 1. Ross, Michael H., Gordon I. Kaye, and Wojciech Pawlina. Histology a text and atlas. 4th edition. 2003. ISBN 0 683 30242 6. Category Tooth development dentistry stub Tooth development ja ... more details
In mathematics, stratified Morse theory is an analogue to Morse theory for general topologically stratified space stratified spaces , originally developed by Mark Goresky and Robert MacPherson mathematician Robert MacPherson . The main point of the theory is to consider functions math f M to mathbb R math and consider how the stratified space math f 1 infty,c math changes as the real number math c in mathbb R math changes. Morse theory of stratified spaces has uses everywhere from pure mathematics topics such as braid groups and Lawrence Krammer representation representations to robot motion planning and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. See also Digital Morse theory Discrete Morse theory Morse theory Level set method References Stratified Morse theory , by M. Goresky and R. MacPherson Springer Verlag, Berlin, Heidelberg, New York, 1988, xiv 272 pp. http www.math.ias.edu goresky pdf SMT.djvu DJVU file on Goresky s page D. Handron, Generalized billiard paths and Morse theory on manifolds with corners. Topology and its Applications, Volume 126, Number 1, 30 November 2002 , pp. 83&ndash 118 36 S.A. Vakhrameev, Morse lemmas for smooth functions on manifolds with corners. Dynamical systems, 8. J. Math. Sci. New York 100 2000 , no. 4, 2428&ndash 2445. Category Singularity theory Category Generalized manifolds Category Morse theory topology stub ... more details
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