Unreferenced date December 2009 about mathematics In mathematics , connectedness is used to refer to various properties meaning, in some sense, all one piece . When a mathematical object has such a property, we say it is connected otherwise it is disconnected . When a disconnected object can be split naturally into connected pieces, each piece is usually called a component or connected component . Connectedness in topology Main Connected space A topological space is said to be connected space connected if it is not the union of two disjoint nonempty open set s. A Set mathematics set is open if it contains no point lying on its boundary topology boundary thus, in an informal, intuitive sense, the fact that a space can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces. Other notions of connectedness Fields of mathematics are typically concerned with special kinds of objects. Often such an object ... it is convenient to restate the definition of connectedness in such fields. For example, a graph ... a context free measure of connectedness, called the clustering coefficient . Other fields of mathematics ... of connectedness often reflect the topological meaning in some way. For example, in category ..., all one piece. There may be different notions of connectedness that are intuitively ... out to be different from standard topological connectedness in particular, there are connected topological ... that are related to, but clearly different from, connectedness. For example, a path connected topological ... graph theory Properties and parameters based on the idea of connectedness often involve the word ... integer k for which the graph is k connected. While terminology varies, noun forms of connectedness ... spaces, it is far more common to speak of simple connectivity than simple connectedness . On the other ... as a synonym for connectedness . Another example of connectivity can be found in regular tilings ... more details
Deligne s connectedness theorem Fulton Hansen connectedness theorem Grothendieck s connectedness theorem Zariski s connectedness theorem Zariski s main theorem disambig ... more details
Unreferenced date December 2009 In one dimensional complex dynamics , the Connected space connectedness locus mathematics locus in a parameter space of polynomials or rational functions consists of those parameters for which the corresponding Julia set is connected. Without doubt, the most famous connectedness locus is the Mandelbrot set , which arises from the family math f c z z 2 c , math of complex quadratic polynomial s. The connectedness loci of the higher degree unicritical families, math z mapsto z d c , math where math d geq 3 , math are often called Multibrot set s . For these families, the bifurcation locus is the boundary of the connectedness locus. This is no longer true in settings, such as the full parameter space of cubic polynomials, where there is more than one free critical point mathematics critical point . For these families, even maps with disconnected Julia sets may display nontrivial dynamics. Hence here the connectedness locus is generally of less interest. DEFAULTSORT Connectedness Locus Category Fractals ... more details
DISPLAYTITLE lambda connectedness In applied mathematics , lambda connectedness or &lambda connectedness deals with partial connectivity for a discrete space . Assume that a function on a discrete space usually a graph is given. A degree of connectivity connectedness will be defined to measure the connectedness of the space with respect to the function. It was invented to create a new method for image Segmentation image processing segmentation . The method has expanded to handle other problems related to uncertainty for incomplete information analysis. ref name lambda connectedness L. Chen, O. Adjei, D. Cooley, lambda connectedness Method and Applications, Proc. IEEE Conf on System, Man and Cybernetics 2000, pp 1157 1562, 2000. ref ref name lambda connectedness1 L. Chen, O. Adjei, lambda connectedness and its applications, Journal of Scientific and Practical Computing Vol.3, No.1 2009 19 52 . ref For a digital image and a certain value of math lambda math , two pixels are called math lambda math connected if there is a path linking those two pixels and the connectedness of this path is at least math lambda math . math lambda math connectedness is an equivalence relation. ref name fuzzy ... classification, Information Sciences Applications, Vol 1, No 2, pp 77 95, 1994. ref Background Connectedness ... or no connection. lambda connectedness is introduced to measure incomplete or fuzzy relations ... among these vertices and are usually obtained from outside of the system. math lambda math connectedness ... weights. In order to define a partial, incomplete, or fuzzy connectedness, one needs to assign ... or economic network. Basic concepts A generalized definition of math lambda math connectedness ... connectedness for any two points. Assume math alpha rho x,y math is used to measure the neighbor connectivity ... n min alpha rho x i,x i 1 i 1, ldots,n 1 math Finally, the degree of connectedness connectivity of two ... math connectedness is a equivalence relation. It can be used in image segmentation. References reflist ... more details
File A photo of a lake.png thumb right Nature connectedness is the extent that an individual includes ... of nature connectedness are similar to those of a personality trait nature connectedness ... Schultz ref name Schultz describes three components that make up the nature connectedness construct The cognitive component is the core of nature connectedness and refers to how integrated one feels ... up nature connectedness and are required for a healthy relationship with nature. If an individual ... ref name Mayer2 Other researchers describe the nature connectedness construct in a simpler manner. For instance, nature connectedness can be thought of as a love of nature also referred to as emotional ... 10.1177 00139169921972056 ref Similarly, nature connectedness can be defined as how much a person ... feeling emotionally connected with nature. ref name Mayer1 Nature connectedness as a construct ..., E. A. 2008 . The distinction between humans and nature Human perceptions of connectedness to nature ... of nature connectedness is also related to a branch of psychology called ecopsychology . This branch ... to nature. The three main scales are Nature Relatedness, Nature Connectedness, and Inclusion of Nature ... CUHL webpage for a copy of the scale. The Connectedness to Nature Scale CNS . ref name Mayer1 Mayer, F. S., & Frantz, C. M. 2004 . The nature connectedness scale A measure of individuals feeling ..., K. 2009 . Why is nature beneficial? The role of connectedness to nature. Environment and Behavior .... See also Connectedness to nature scale . Inclusion of Nature in Self Scale INS ref name Schultz ... Test Nature. For more ways to measure nature connectedness please visit http www.conpsychmeasures.com ... suggesting they are all part of the nature connectedness construct. ref name Howell Howell, A. J., Dopko, R. L., Passmore, H., & Buro, K. 2011 . Nature connectedness Associations with well being and mindfulness ... connectedness as a personality trait In personality psychology, researchers have generally agreed ... more details
Cleanup date February 2008 1. Social connectedness has multiple aspects. Fundamentally it is about people relating to other people. It is about how people come together, interact and network. It is also one component of several of community cohesion. The benefits from social connectedness can accrue to the individual and to society. Social connectedness doesn t just include individual level concepts as below in the psychological sense but also about relationships with and between family, friends, colleagues, neighbours, paid work, sport and other leisure activities, community work and wider communities. Population based surveys sometimes use qualitative questions to help understand the level of social connectedness in communities ref Quigley and Thornley, 2011 ref . 2. Social connectedness is also a psychological term used to describe the quality and number of connections we have with other people in our social circle of family , friend s and acquaintance s. These connections can be both in real life , as well as online. The more socially connected a person is in his life, generally the greater sense of self control and self determination he feels. Fact date May 2009 Zero Acquaintance defines as Observation and judgment of someone with whom one has never interacted . ref Friedman & Schustack, 2009, p. 279 ref Components There are six components that have been shown to help a person determine the quality of his interactions and psychological defined social connectedness with others Duration of relationship Frequency of interaction with the other person Knowledge of the other person s goals Physical intimacy or closeness with the other person Self disclosure to the other person Social network familiarity how familiar is the other person with the rest of your social circle The higher a person scores on these components, the greater the quality of his social connectedness ... measure their connectedness with another individual. Footnotes reflist Further Reading & References ... more details
The connectedness to nature scale is a measure of individuals trait levels of feeling emotionally connected to the natural world in the realm of social and environmental psychology . The CNS is being used to test the effects of situational factors and personality characteristic that might impact connection to nature. A study by Mayer and Frantz 2004 found the CNS to be a significant predictor of ecological behavior and subjective well being ref cite journal last Mayer first F. Stephan coauthors Cynthia McPherson Frantz year 2004 title The connectedness to nature scale A measure of individuals feeling in community with nature journal Journal of Environmental Psychology volume 24 issue 4 pages 503 515 ref . References reflist Category Emotion Category Environmental psychology social psych stub ... more details
In mathematics , the Fulton Hansen connectedness theorem is a result from intersection theory in algebraic geometry , for the case of subvarieties of projective space with codimension large enough to make the intersection have components of dimension at least 1. The formal statement is that if V and W are irreducible algebraic subvarieties of a projective space P , all over an algebraically closed field , and if dim V dim W dim P in terms of the dimension of an algebraic variety , then the intersection U of V and W is connected space connected . More generally, the theorem states that if math Z math is a projective variety and math f Z to P n times P n math is any morphism such that math dim f Z n math , then math f 1 Delta math is connected, where math Delta math is the diagonal in math P n times P n math . The special case of intersections is recovered by taking math Z V times W math , with math f math the natural inclusion. See also Zariski s connectedness theorem Grothendieck s connectedness theorem Deligne s connectedness theorem References citation first W. last Fulton first2 J. last2 Hansen title A connectedness theorem for projective varieties with applications to intersections and singularities of mappings journal Annals of Math. volume 110 year 1979 pages 159 166 doi 10.2307 1971249 jstor 1971249 issue 1 publisher Annals of Mathematics citation first R. last Lazarsfeld title Positivity in Algebraic Geometry publisher Springer year 2004 External links http www.math.unizh.ch fileadmin math preprints 20 05.pdf PDF lectures withe the result as Theorem 15.3 attributed to Faltings, also Category Intersection theory Category Theorems in algebraic geometry ... more details
In mathematics, Grothendieck s connectedness theorem harvnb Grothendieck 2005 loc XIII.2.1 , harvnb Lazarsfeld 2004 loc theorem 3.3.16 states that if A is a complete local ring whose spectrum is k connected and f is in the maximal ideal, then Spec A fA is k &minus 1 connected. Here a Noetherian scheme is called k connected if its dimension is greater than k and the complement of every closed subset of dimension less than k is connected. Grothendieck XIII.2.1 It is a local analogue of Bertini s theorem . References citation last Grothendieck first Alexandre authorlink Alexandre Grothendieck first2 Mich le last2 Raynaud title S minaire de G om trie Alg brique du Bois Marie 1962 Cohomologie locale des faisceaux coh rents et th or mes de Lefschetz locaux et globaux SGA 2 series Documents Math matiques 4 origyear 1968 edition Updated year 2005 publisher Soci t Math matique de France language French pages x 208 isbn 2 85629 169 4 citation title Positivity in Algebraic Geometry first Robert last Lazarsfeld year 2004 publisher Springer isbn 3540225331 Category Theorems in algebraic geometry ... more details
About the word the film Kanyini film Kanyini is an Indigenous Australians Australian Indigenous word. Kanyini is the principle of connectedness through caring and responsibility that underpins Aboriginal life. Kanyini is a connectedness to tjukurrpa knowledge of creation or Dreaming spirituality Dreaming , spirituality , ngura place, land , walytja kinship and kurunpa spirit or soul . Kanyini is nurtured through caring and practicing responsibility for all things. See also Nurture kinship References http www.resurgence.org magazine article132 Kanyini.html Resurgence Magazine Kanyini by Bob Randall Category Indigenous Australian culture Category Australian Aboriginal culture Ia lang stub ... more details
In mathematics , especially in the field of commutative algebra , a connected ring is a commutative ring A that satisfies one of the following equivalent conditions A possesses no non trivial that is, not equal to 1 or 0 idempotent elements the Spectrum of a ring spectrum of A is a connected space . Examples and non examples Connectedness defines a fairly general class of commutative rings. For example, all local ring s and all irreducible ring s are connected. In particular, all integral domain s are connected. Non examples are given by product rings such as Z × Z here the element 1, 0 is a non trivial idempotent. Generalizations In algebraic geometry , connectedness is generalized to the concept of a connected scheme . Category Commutative algebra Category Ring theory ... more details
Unreferenced date December 2006 orphan date November 2009 In topology , a hereditarily unicoherent , Connected space Path connectedness arcwise connected continuum topology continuum is called a dendroid. A continuum X is called hereditarily unicoherent if every subcontinuum of X is unicoherent . A locally connected dendroid is called a dendrite mathematics dendrite . DEFAULTSORT Dendroid Topology Category Continuum theory Topology stub ... more details
In statistics , m separation is a measure of disconnectedness in ancestral graph s and a generalization of d separation for directed acyclic graph s. It is the opposite of m connectedness . Suppose G is an ancestral graph. For given source and target nodes s and t and a set Z of nodes in G s , t , m connectedness can be defined as follows. Consider a path graph theory path from s to t . An intermediate node on the path is called a collider if both edges on the path touching it are directed toward the node. The path is said to m connect the nodes s and t , given Z , if and only if every non collider on the path is outside Z , and for each collider c on the path, either c is in Z or there is a directed path from c to an element of Z . If s and t cannot be m connected by any path satisfying the above conditions, then the nodes are said to be m separated . The definition can be extended to node sets S and T . Specifically, S and T are m connected if each node in S can be m connected to any node in T , and are m separated otherwise. References Drton, Mathias and Thomas Richardson. Iterative Conditional Fitting for Gaussian Ancestral Graph Models . http www.stat.washington.edu www research reports 2003 tr437.pdf Technical Report 437 , December 2003. See also d separation Category Graphical models ... more details
In mathematics , a complete manifold or geodesically complete manifold is a Pseudo Riemannian manifold pseudo Riemannian manifold for which every maximal inextendible geodesic is defined on math mathbb R math . Examples All compact space compact manifolds and all homogeneous space homogeneous manifolds are geodesically complete. Euclidean space math mathbb R n math , the sphere s math mathbb S n math and the torus tori math mathbb T n math with their usual Riemannian metric s are all complete manifolds. A simple example of a non complete manifold is given by the punctured plane math M mathbb R 2 setminus 0 math with its usual metric . Geodesics going to the origin cannot be defined on the entire real line. Path connectedness, completeness and geodesic completeness It can be shown that a finite dimensional Connected space Path connectedness path connected Riemannian manifold is a complete metric space if and only if it is geodesically complete. This is the Hopf Rinow theorem . This theorem does not hold for infinite dimensional manifolds. The example of a non complete manifold the punctured plane given above fails to be geodesically complete because, although it is path connected, it is not a complete metric space any sequence in the plane converging to the origin is a non converging Cauchy sequence in the punctured plane. References Citation last1 O Neill first1 Barrett title Semi Riemannian Geometry publisher Academic Press isbn 0 12 526740 1 year 1983 . See chapter 3, pp. 68 . DEFAULTSORT Complete Manifold Category Riemannian geometry Category Manifolds ... more details
In psychology , the care perspective focuses on people in terms of their connectedness with others, communication interpersonal communication , relationships with others, and concern for others. ref cite book title Moral Theory An Introduction author Mark Timmons year 2002 publisher Rowman & Littlefield url http books.google.com books?vid ISBN084769769X&id 3yqoMaokIFAC&pg RA2 PA225&lpg RA2 PA225&dq 22Care perspective 22&ie ISO 8859 1&output html isbn 0 8476 9769 X ref See also Carol Gilligan Moral development References reflist Category Human communication social psych stub ... more details
In topology and related areas of mathematics a uniformly connected space or Cantor connected space is a uniform space U such that every uniformly continuous function from U to a discrete uniform space is constant. A uniform space U is called uniformly disconnected if it is not uniformly connected. Properties A compact space compact uniform space is uniformly connected if and only if it is connected space connected Examples every connected space is uniformly connected the rational number s and the irrational numbers are disconnected but uniformly connected See also connectedness References Georg Cantor Cantor, Georg ber Unendliche, lineare punktmannigfaltigkeiten , Mathematische Annalen . 21 1883 545 591. topology stub Category uniform spaces ... more details
No footnotes date April 2009 Classical Adlerian individual psychotherapy , brief therapy, couple therapy, and family therapy follow parallel paths. Clients are encouraged to overcome their feelings of insecurity, develop deeper feelings of connectedness, and to redirect their striving for significance into more socially beneficial directions. Through a respectful Socratic dialogue , they are challenged to correct mistaken assumptions, attitudes, behaviors and feelings about themselves and the world. Constant encouragement stimulates clients to attempt what was previously felt as impossible. The growth of confidence, pride, and gratification leads to a greater desire and ability to cooperate. The objective of Classical Adlerian psychotherapy is to replace exaggerated self protection, self enhancement, and self indulgence with courageous social contribution. See also Classical Adlerian psychology Adlerian Alfred Adler Individual psychology External links http www.alfredadler.org Category Psychological schools Adlerian Category Psychiatric treatments psychology stub ... more details
orphan date January 2008 The nursing diagnosis readiness for enhanced spiritual well being is defined as an ability to experience and integrate meaning and purpose in life through a person s connectedness with self, others art, music, literature, nature, or a power greater than oneself. Anonymous, 2002, p. 68 and was approved by NANDA in 2002. Defining characteristics A person with this diagnosis may Having an enhanced desire for hope Feel that there is meaning and purpose to their life Have a sense of peace or serenity Surrender love Be forgiving towards themself, and request forgiveness of others Request forgiveness from others Have a satisfying philosophy of life Experience joy, courage, or heightened coping Pray or meditate Connect with others Provide service to others Experience connections with nature Experience connections with or a desire to create art, music, or literature, particularly of a religious or spiritual nature Experience a connection with a power greater than oneself Report mystical experiences or Participate in religious activities. Sources Anonymous 2002 . Diagnosis Review Committee New and revised diagnoses. Nursing Diagnosis 13 2 p. 68 71. Philadelphia NANDA Category Nursing diagnoses ... more details
The Whitehead conjecture is a claim in algebraic topology . It was formulated by J. H. C. Whitehead in 1941. It states that every Connectedness connected subcomplex of a two dimensional Aspherical space aspherical CW complex is aspherical. In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the Eilenberg Ganea conjecture , or there must be a counterexample to the Whitehead conjecture. References http links.jstor.org sici?sici 0003 486X 28194104 292 3A42 3A2 3C409 3AOARTHG 3E2.0.CO 3B2 5 J. H. C. Whitehead, On adding relations to homotopy groups , Annals of Mathematics, 2nd Ser., 42 1941 , no. 2, 409 &ndash 428. http www.springerlink.com content nhj24dgb0vb7bx5p ?p 3b9c54d35a7c445587b1fc97576a6a83&pi 1 Mladen Bestvina, Noel Brady, Morse theory and finiteness properties of groups , Inventiones Mathematicae 129 1997 , no. 3, 445 &ndash 470. DEFAULTSORT Whitehead Conjecture Category Theorems in algebraic topology Category Conjectures ... more details
set closed in 0, 1 contradicting the connected space connectedness of this set. Clearly we ... , r × R B r , &infin × R will form a separated sets separation on f U contradicting the connectedness ... 2nd publisher Prentice Hall isbn 0 13 181629 2 Cite journal title Connectedness series Encyclopedic ... more details
notability date January 2011 primarysources date January 2011 The Boreal Forest Learning Centre BFLC is a non profit organization designed to promote awareness and stewardship of Saskatchewan s Boreal Forest . The goal of the BFLC is to bring together First Nations Elders, Educators and Canadian Parks and Wilderness Society to broaden perspectives of inter connectedness. The BFLC offers curriculum based workshops, guided tours into the boreal forest and developing recreational trails. Other projects include working with Prince Albert National Park to protect Bison , land use and mapping as well as identifying native plants and their uses. See also Prairie Learning Centre External links https sites.google.com a saskborealforestlearningcentre.org saskatchewan boreal forest learning centre Home about us Boreal Forest Learning Centre http www.prairielearningcentre.ca Prairie Learning Centre http www.parkscanada.gc.ca princealbert Prince Albert National Park Category Organizations based in Saskatchewan ... more details
space. As an example, the notion of weak local connectedness at a point and its relation to local connectedness will be considered later on in the article. In the latter part of the twentieth century ... is far more complex. From this modern perspective, the stronger property of local path connectedness ... be connected and locally path connected. Local path connectedness will be discussed as well. A space ... connectedness at x we require a neighborhood base of open connected sets, whereas for weak local connectedness at x we require only a base of neighborhoods of x . Evidently a space which ... Seebach, pp. 49 50 ref Further examples are given later on in the article. Properties 1. Local connectedness ... connectedness. In particular 2. A space is locally connected if and only if it admits a base ... x math and thus math QC x C x math . Since local path connectedness implies local connectedness, it follows ... More on local connectedness versus weak local connectedness Theorem Let X be a weakly locally connected ... on Connectedness Im Kleinen first H. S. last Davis journal Proceedings of the American Mathematical ... more details
open topology open subsets. Connectedness is one of the principal topological properties that is used ... of two rings in a nontrivial way. Path connectedness This section is linked from Covering space and path ... or C sup n sup are connected if and only if they are path connected. Additionally, connectedness and path connectedness are the same for Wiktionary finite finite topological spaces. Arc connectedness Connected space Arc connectedness redirects to this subsection A space X is said to be arc connected ... space . Clearly 0 and 0 can be connected by a path but not by an arc in this space. Local connectedness ... of connectedness can be formulated independently of the topology on a space. To wit, there is a category .... Stronger forms of connectedness There are stronger forms of connectedness for topological space s, for instance ... however, that if the path connectedness requirement is dropped from the definition of simple connectivity ... connected space connected component graph theory n connected Connectedness locus Extremally disconnected ... more details
Noncommutative topology in mathematics is a term applied to the strictly C algebra ic part of the noncommutative geometry program. The program has its origins in the Gel fand duality between the topology of locally compact spaces and the algebraic structure of commutative operation commutative C algebra s. Several topological properties can be formulated as properties for the C algebra s without making reference to commutative operation commutativity or the underlying space , and so have an immediate generalization. Amongst these are compact space compactness being unital algebra unital , dimension real rank real or stable rank , connected space connectedness projectionsless algebra projectionless algebra and K theory . So we think of a noncommutative C algebra as the algebra of functions on a noncommutative space which does not exist classically. A major tool in the field is a functor Bifunctors bivariant version of K theory called KK theory . It has a composition product math KK A,B times KK B,C rightarrow KK A,C math of which the ring structure in ordinary K theory is a special case. The product gives the structure of a Category topology category to KK. It has been related to Correspondence mathematics correspondences of algebraic varieties. ref http arxiv.org abs math.QA 0512138 math.QA 0512138 ref Notes references DEFAULTSORT Noncommutative Topology Category Banach algebras Category Topology topology stub ... more details
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