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	homeomorphism - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "homeomorphism" is defined.
		homeomorphism : The American Heritage® Dictionary of the English Language [home, info]
		Homeomorphism : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=homeomorphism (112 words)

	Homeomorphism - Wikipedia, the free encyclopedia
		Roughly speaking a topological space is a geometric object and the homeomorphism is a continuous stretching and bending of the object into a new shape.
		Intuitively a homeomorphism maps points in the first object that are "close together" to points in the second object that are close together, and points in the first object that are not close together to points in the second object that are not close together.
		This characterization of a homeomorphism often leads to confusion with the concept of homotopy, which is actually defined as a continuous deformation, but from one function to another, rather than one space to another.
	en.wikipedia.org /wiki/Homeomorphism (753 words)

	Local homeomorphism - Wikipedia, the free encyclopedia
		In topology, a local homeomorphism is a map from one topological space to another that respects locally the topological structure of the two spaces.
		This is a local homeomorphism for all non-zero n, but a homeomorphism only in the cases where it is bijective, i.e.
		All covering maps are local homeomorphisms; in particular, the universal cover p : C → X of a space X is a local homeomorphism.
	en.wikipedia.org /wiki/Local_homeomorphism (426 words)

	Local homeomorphism
		Then this is a local homeomorphism for all non-zero n, but a homeomorphism only in the cases where it is bijective, i.e.
		All covering maps are local homeomorphisms; in particular, the universal cover p : C → X of a space X is a local homeomorphism.
		A bijective local homeomorphism is therefore a homeomorphism.
	www.sciencedaily.com /encyclopedia/local_homeomorphism (517 words)

	Knowledge King - Homeomorphism (Site not responding. Last check: 2007-10-08)
		If two objects are homeomorphic, one can find a continuous function which maps points from the first object to corresponding points of the second object, and vice versa.
		Such a function is called a homeomorphism; intuitively, it maps points in the first object that are "close together" to points in the second object that are close together, and points in the first object that are not close together to points in the second object that are not close together.
		As such, the composition of two homeomorphisms is again a homeomorphism, and the set of all homeomorphisms X → X forms a group.
	www.knowledgeking.net /encyclopedia/h/ho/homeomorphism.html (637 words)

	Local homeomorphism -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (The configuration of a communication network) topology, a local homeomorphism is a (A diagrammatic representation of the earth's surface (or part of it)) map from one ((mathematics) any set of points that satisfy a set of postulates of some kind) topological space to another that respects locally the topological structure of the two spaces.
		This is a local homeomorphism for all non-zero n, but a homeomorphism only in the cases where it is (Click link for more info and facts about bijective) bijective, i.e.
		The local homeomorphisms with (Click link for more info and facts about codomain) codomain Y stand in a natural 1-1 correspondence with the (Click link for more info and facts about sheaves) sheaves of sets on Y.
	www.absoluteastronomy.com /encyclopedia/l/lo/local_homeomorphism.htm (585 words)

	Homeomorphism -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Homeomorphisms are the ((biology) similarity or identity of form or shape or structure) isomorphisms in the (Click link for more info and facts about category of topological spaces) category of topological spaces.
		As such, the composition of two homeomorphisms is again a homeomorphism, and the set of all self-homeomorphisms X → X forms a ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule) group, called the homeomorphism group of X, often denoted Homeo(X).
		This characterization of a homeomorphism often leads to confusion with the concept of (Click link for more info and facts about homotopy) homotopy, which is actually defined as a continuous deformation, but from one function to another, rather than one space to another.
	www.absoluteastronomy.com /encyclopedia/h/ho/homeomorphism.htm (999 words)

	Encyclopedia: Homeomorphism (Site not responding. Last check: 2007-10-08)
		In the mathematical field of topology a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
		In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
		Topology In topology, a local homeomorphism is a map from one topological space to another that respects locally the topological structure of the two spaces.
	www.nationmaster.com /encyclopedia/Homeomorphism (1946 words)

	Homeomorphism (Site not responding. Last check: 2007-10-08)
		A hollow sphere containing a smaller solid ball is homeomorphic to a hollow cube with a solid cubeoutside of it.
		As such, the composition of two homeomorphisms is again ahomeomorphism, and the set of all homeomorphisms X → X forms a group.
		This characterization of a homeomorphism often leads to confusion with the concept of homotopy, which is actually defined as a continuous deformation, but from one function toanother, rather than one space to another.
	www.therfcc.org /homeomorphism-35844.html (603 words)

	Mathematics
		On the local representation of G-closure, 1999, 20 pp.
		ACL homeomorphisms and linear dilatation, 2000, 8 pp.
		The local homeomorphism property of spatial quasiregular mappings with distortion close to one, 2004, 29 pp.
	www.math.jyu.fi /research/papers.html (1324 words)

	Local homeomorphism: Definition and Links by Encyclopedian.com - All about Local homeomorphism (Site not responding. Last check: 2007-10-08)
		In topology, a local homeomorphism is a map f from one topological space X to another, Y, that respects locally the topological structure.
		More precisely, for all points x of X there should be an open neighbourhood N of x, such that f(N) is open in Y and f restricted to N is a homeomorphism from N to f(N).
		on an open disk round 0 is not a local homeomorphism at 0 when n is at least 2.
	www.encyclopedian.com /lo/Local-homeomorphism.html (304 words)

	Local homeomorphism (Site not responding. Last check: 2007-10-08)
		It is shown in complex analysis that a complex analytic function f gives a local homeomorphism precisely when the derivative f'(z) is non-zero for all z in the domain off.
		All covering maps are local homeomorphisms; in particular, the universal cover p : C → X of a spaceX is a local homeomorphism.
		The local homeomorphisms with codomain Y stand in a natural 1-1correspondence with the sheaves of sets on Y.
	www.therfcc.org /local-homeomorphism-206650.html (427 words)

	Sheaf - Open Encyclopedia (Site not responding. Last check: 2007-10-08)
		Suppose X is a topological space, and C is a category (often, this is the category of sets, the category of Abelian groups, the category of commutative rings, or the category of modules over a fixed ring).
		Schemes are special locally ringed spaces important in algebraic geometry; sheaves of modules are important in the associated theory.
		Its local behavior on the interval where it is one is that of a constant function, but knowing that a bump function is the constant one near a given point does not tell you where the function begins to decay; from its local behavior, you cannot even conclude that it is a bump function!
	open-encyclopedia.com /Sheaf (2463 words)

	fibration (Site not responding. Last check: 2007-10-08)
		Because a sheaf is 'as good as' a local homeomorphism, the notions seemed closely interlinked at the time.
		We are not in this case given a local cartesian product structure (which defines the more restricted fiber bundle case), but something possibly weaker that still allows 'sideways' movement from fiber to fiber.
		One of the main desirable properties of the Serre spectral sequence is to account for the action of the fundamental group of the base X on the homology of the total space Y.
	www.yourencyclopedia.net /fibration.html (396 words)

	Homeomorphism (Site not responding. Last check: 2007-10-08)
		Una esfera hueco que contiene una bola sólida más pequeña es homeomorphic a una esfera hueco con una bola sólida afuera de ella.
		Si dos objetos son homeomorphic, uno puede encontrar una función contínua que traz puntos del primer objeto a los puntos correspondientes del segundo objeto, y viceversa.
		Esta caracterización de un homeomorphism conduce a menudo a la confusión con el concepto de homotopy, que se define realmente como deformación contínua, pero a partir de una función a otra, más bien que a un espacio a otro.
	www.yotor.net /wiki/es/ho/Homeomorphism.htm (661 words)

	sciforums.com - some basic questions
		a space is n dimensional iff there is a local homeomorphism between that space and Rn.
		a homeomorphism is a mapping that takes close points on the domain space to close points in the range space, and vice versus.
		a local homeomorphism means that for any point, i can find a homeomorphism of some neighborhood, some small interval, to Rn.
	www.sciforums.com /showthread.php?t=13735 (2113 words)

	Talk:Sheaf (mathematics) - Wikipedia, the free encyclopedia
		The point on terminology as I'd see it is to use local homeomorphism consistently for étale here: so that the étale cohomology page doesn't have to start by saying that étale needs disambiguation.
		No article yet on local systems of coefficients, which were an important case in the formulation.
		For example I take the bundle R x R, F at a point P will be the ring of all germs of continuous functions at P (see local ring).
	www.wikipedia.org /wiki/Talk:Sheaf (1435 words)

	Orientable manifold - Wikipedia, the free encyclopedia
		To make topological sense of the notion of orientation, one can use the idea of covering space (see local homeomorphism).
		For a connected manifold M one defines a covering space M, also a manifold, and a 2-to-1 local* homeomorphism from M* to M.
		The two points of M* mapping to a given p in M are the two orientations of a small open ball near p.
	en.wikipedia.org /wiki/Orientable_manifold (652 words)

	On Local Homeomorphism of Mapping ... (Site not responding. Last check: 2007-10-08)
		On local homeomorphism of mapping with bounded distortion with the coefficient of distortion close to identity
		In 1971 V. Goldshtein has proved a theorem about local homeomorphism of mappings with bounded distortion with the coefficient of distortion close to identity.
		The problem is that the structure of 1-quasiregular mappings is unknown on an arbitrary Carnot group.
	www.mat.utfsm.cl /publicaciones/preprints2002/11-Local (139 words)

	Station Information - Sheaf space
		This article should be merged with local homeomorphism.
		Given two topological spaces E and X and a continuous map π:E->X, E is an étale space over X (with respect to π) if π is a local homeomorphism.
		In other words, for every element x of E, there exists a neighborhood of it such that π restricted to this neighborhood is a homeomorphism to an open subset of X. See also covering map, sheaf.
	www.stationinformation.com /encyclopedia/s/sh/sheaf_space.html (81 words)

	PlanetMath: covering space (Site not responding. Last check: 2007-10-08)
		Covering maps are especially important in the study of Riemann surfaces; in this context, one sometimes discusses a generalized notion of covering map called a ``ramified covering''; this allows one to replace a discrete set of the local homeomorphisms by maps that locally look like
		Covering maps are also generalized in algebraic geometry; there the corresponding notion is that of étale morphism.
		Note that this is a completely separate usage of the word ``cover'' than we encounter in ``open cover''; confusion usually does not arise.
	planetmath.org /encyclopedia/CoveringMap.html (259 words)

	Homeomorphism: Definition and Links by Encyclopedian.com - All about Homeomorphism (Site not responding. Last check: 2007-10-08)
		Homeomorphism: Definition and Links by Encyclopedian.com - All about Homeomorphism
		If two objects are homeomorphic, one can find a function which maps points from the first object to corresponding points of the second object, and vice versa.
		The intuitive criterion of stretching, bending, cutting and glueing back together takes a certain amount of practice to apply correctly--it is not obvious from the above description that deforming a line segment to a point is impermissable, for instance.
	www.encyclopedian.com /ho/Homeomorphism.html (644 words)

	Encyclopedia: Local diffeomorphism (Site not responding. Last check: 2007-10-08)
		In mathematics, a local diffeomorphism is a smooth map f : M → N between smooth manifolds such that for every point p of M there exists an open neighbourhood U of p such that f(U) is open in N and f
		Every local diffeomorphism is also a local homeomorphism and therefore an open map.
		A diffeomorphism is just a bijective local diffeomorphism.
	www.nationmaster.com /encyclopedia/Local-diffeomorphism (481 words)

	[No title]
		7, 1029-1033 (1983) #2239 1983a 4 3 1 n shen, zuhe a computationally verifying sufficient condition for local homeomorphism (in chinese) j.
		84/10, 77-85 (1984) #2240 1984a 3 2 1 n shen, zuhe on the global homeomorphism (in chinese) j.
		85/7, 37-47 (1985) #3042 1987 5 4 2 n shen, zuhe zhu, yiran an interval version of shubert's iterative method for the localization of the global maximum computing 38, 275-280 (1987) #2245 1986 8 5 2 n shi, zhi-cheng gao, wei-bin a necessary and sufficient condition for the positive-definiteness of interval symmetric matrices internat.
	www.mat.univie.ac.at /~neum/intlib/autr-z.txt (13940 words)

	Subobject classifier - Wikipedia, the free encyclopedia
		For the topos of sheaves of sets on a topological space X, it can be described in these terms: take the disjoint union Ω of all the open sets U of X, and its natural mapping π to X coming from all the inclusion maps.
		Then π is a local homeomorphism, and the sheaf corresponding is the required subobject classifier (in other words the construction of Ω is by means of its espace étalé).
		One can also consider Ω to be, in a (tautological) sense, the graph of the membership relation obtaining between points x of X and open sets U.
	www.wikipedia.org /wiki/Sub-object_classifier (302 words)

	Team-Apics
		Finally, certain control problems, such as path planning, are not of a local nature and cannot be answered via a linear approximation.
		The success of the linear model, in control or in identification, is due to the deep understanding one has of it; in the same fashion, a refined knowledge of invariants of non-linear systems under basic transformations is a prerequisite for a theory of non-linear identification and control.
		From the algebraic-differential point of view, the module of differentials of a controllable system is free and of finite dimension over the ring of differential polynomials in d/dt with coefficients in the space of functions of the system, and for which a basis can be explicitly constructed [23].
	www.inria.fr /rapportsactivite/RA2004/apics/uid23.html (1189 words)

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