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Topic: Metrizable

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	PlanetMath: completely metrizable
		is said to be completely metrizable if there is a metric
		In particular, a completely metrizable space is metrizable.
		This is version 1 of completely metrizable, born on 2002-01-24.
	www.planetmath.org /encyclopedia/CompletelyMetrizable.html (48 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-09-25)
		For the metrizability of the space of a topological group it is necessary and sufficient that the group satisfies the first axiom of countability; moreover, the space is then metrizable by an invariant metric (for example, with respect to left multiplication).
		An important topological property of a space metrizable by a complete metric is the Baire property: The intersection of any countable family of everywhere-dense open sets is everywhere dense.
		Metrizability criterion 1) is due to R.H. Bing [a1].
	eom.springer.de /m/m063730.htm (960 words)

	On Paracompactness of Metrizable Spaces - Borys, metrizable, of, Mathematics, mizar, JFM, pcomps, The, have ...
		On Paracompactness of Metrizable Spaces - Borys, metrizable, of, Mathematics, mizar, JFM, pcomps, The, have (ResearchIndex)
		@misc{ borys91paracompactness, author = "L. Borys and P. metrizable and s of and F. Mathematics and h mizar and o JFM and V. pcomps and h The and p have", title = "on paracompactness of metrizable spaces", text = "Leszek Borys.
		1 on paracompactness of metrizable spaces - Borys, metrizable et al.
	citeseer.ist.psu.edu /362617.html (546 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-09-25)
		Initially, uniform spaces were used as tools for the study of the topologies (generated by them) (similar to the way a metric on a metrizable space was often used for the study of the topological properties of the space).
		The topology of a metrizable uniform space is paracompact, by Stone's theorem.
		The construction of a metrizable uniform space that is not uniformly paracompact (i.e.
	eom.springer.de /u/u095250.htm (1278 words)

	Transactions of the American Mathematical Society
		Extension theory of separable metrizable spaces with applications to dimension theory
		Abstract: The paper deals with generalizing several theorems of the covering dimension theory to the extension theory of separable metrizable spaces.
		is a separable metrizable space of finite dimension and
	www.ams.org /tran/2001-353-01/S0002-9947-00-02536-8/home.html (566 words)

	Metrization theorem - Wikipedia, the free encyclopedia
		In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
		Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable.
		An example of a space that is not metrizable is the real line with the lower limit topology.
	en.wikipedia.org /wiki/Metrization_theorems (454 words)

	Metrizable Topology -- from Wolfram MathWorld
		Special metrizability criteria are known for Hausdorff spaces.
		A compact Hausdorff space is metrizable iff the set of all elements
		The continuous image of a compact metric space in a Hausdorff space is metrizable.
	mathworld.wolfram.com /MetrizableTopology.html (207 words)

	UC Davis Math: profile_files
		In particular, he is interested in stratifiable spaces and other spaces which have some but not all properties of metrizable spaces.
		The most common objects in topology, such as manifolds, polyhedra, and Euclidean spaces, are metrizable spaces, which means that one can describe the topology by a (real-valued) distance between points, and say that a sequence of points converges to a limit if and only if the distance decreases to zero.
		He showed that a number of basic structure theorems about metrizable spaces, for example that the quotient of a first-countable metrizable space is metrizable, holds for stratifiable spaces also.
	www.math.ucdavis.edu /research/profiles/cborges (245 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-09-25)
		-compactum has a countable base, is metrizable and is even homeomorphic to a closed subset of a segment.
		Any metric on a compactum is complete and totally bounded, and all metrizable spaces having this property are compacta (F.
		Each zero-dimensional metrizable compactum is homeomorphic to some compactum contained in the Cantor set (as a closed subset).
	eom.springer.de /c/c023530.htm (2017 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-09-25)
		In the case of metrizable spaces it is equivalent to Lebesgue's definition.
		The foundations of dimension theory were laid in the first half of the twenties of the 20th century in papers of Urysohn and Menger.
		In the later thirties, the dimension theory of metrizable spaces with a countable base was constructed, and by the start of the sixties the dimension theory of arbitrary metrizable spaces was finished.
	eom.springer.de /D/d032450.htm (2461 words)

	G.M. Reed
		Recall that (1) (V=L) implies that normal locally compact Moore spaces are metrizable and (2) (MA) implies that normal, separable, locally compact Moore spaces have normal squares.
		It is also shown that it is consistent with ZFC and GCH that there exists a normal Moore space with a nonnormal square.
		M(X) is metrizable) implies that X is a \sigma -discrete Moore space with a \sigma -disjoint base.
	www.utm.edu /staff/jschomme/topology/c/a/a/m/48.htm (367 words)

	AMCA: One-point completions of metrizable spaces by Melvin Henriksen (Site not responding. Last check: 2007-09-25)
		If a metrizable space X is a dense in a metrizable space Y, then Y is called a metric extension of X. If T1 and T2 are metric extensions of X and there is a continuous map of T2 into T1 that keeping X pointwise fixed, we write T1<=T2.
		The poset (E(X), <=) of one-point metric extensions of a locally compact metrizable space X is studied.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/m/c/87.htm (288 words)

	Profiles of Women in Mathematics: Mary Ellen Rudin (Site not responding. Last check: 2007-09-25)
		Metrizability in a topological space provides a great deal of structure: a metric space is, for example, paracompact.
		But if one does not require metrizability, and instead asks to what extent normality (assuming all spaces are Hausdorff) achieves the structure of paracompactness, one discovers a very complex world of counterexamples whose product with the closed unit interval is not normal.
		It is undecidable in Zermel-Frankel set theory whether there is a perfectly normal nonmetrizable manifold, and the question of whether every normal Moore space is metrizable has a more complex, unsatisfactory answer.
	www.awm-math.org /noetherbrochure/Rudin84.html (381 words)

	Re: When is a space metrizable
		In Reply to: Re: When is a space metrizable posted by DickT on June 27, 2003 at 19:05:15:
		In Yang Mills theory, matter is defined to be the sections of the associated vector bundles of the representation of the principle bundle over spacetime.
		Re: When is a space metrizable -- bhmtst 7/24/03 (
	www.superstringtheory.com /forum/topboard/messages4/141.html (176 words)

	Gary Gruenhage (Site not responding. Last check: 2007-09-25)
		This question (and also one asking if there is at least a Tychonoff connectification) was stated in a paper of Alas, Tkachuk, Tkacenko, and Wilson, who proved that the answer is positive for separable metric spaces.
		Also, Porter and Woods have shown that every metrizable space with no compact open subsets has a Hausdorff connectification, and Neumann-Lara and Wilson have shown that every strongly 0-dimensional metrizable space has a Tychonoff (orderable) connectification.
		Here we show that a metrizable space X has a metrizable connectification if (and only if) X can be embedded in a metrizable space Y such that every clopen subset of X has a limit point in Y.
	www.utm.edu /staff/jschomme/topology/c/a/a/e/27.htm (252 words)

	[No title] (Site not responding. Last check: 2007-09-25)
		Also, even when spaces are metrizable, it can happen that a metric approach is highly confusing.
		The usual topology of probability distributions on a separable metric space is metrizable, but using metric concepts makes it much harder to understand.
		In many cases of metric spaces, the use of the metric itself confuses the much simpler topological concepts.
	www.math.niu.edu /~rusin/known-math/98/nonmetric (258 words)

	index
		On the relationship between cmp and def in the class of separable metrizable spaces
		Topologies on the autohomeomorphism group of 0-dimensional separable metrizable spaces
		Closure operators in topological groups related to von Neumann's kernel
	www.dmae.upct.es /topology/talks.htm (506 words)

	Metrizable Shape And Strong Shape Equivalences (Site not responding. Last check: 2007-09-25)
		In this paper we construct a functor $\Phi : \pT \to \pA$ which extends Marde\v si\' c correspondence that assigns to every metrizable space its canonical \A-resolution.
		Such a functor allows one to define the strong shape category of prospaces and, moreover, to define a class of spaces, called strongly fibered, that play for strong shape equivalences the role that \A-spaces play for ordinary shape equivalences.
		In the last section we characterize SSDR-promaps, as defined by Dydak and Nowak, in terms of the strong homotopy extension property considered by the author.
	www.intlpress.com /HHA/v4/n1/a6 (91 words)

	HJM, Vol. 26, No. 3, 2000
		For a collection A of metrizable spaces, let P(A) denote the category formed by all finite products of members of A and all their continuous maps.
		For collections A and B indexed by the same set, the categories P(A) and P(B) are compared.
		The results generalize the existence of two metrizable spaces X and Y whose monoids of continuous selfmaps are isomorphic while the categories PX and PY of their finite powers are not.
	www.math.uh.edu /~hjm/Vol26-3.html (1234 words)

	Atlas: On homomorphism spaces of metrizable groups by Gabor Lukacs (Site not responding. Last check: 2007-09-25)
		In this talk we will present a generalization of a result by Chasco, who proved that for every abelian metrizable group G, its dual group [^G] (i.e.
		We prove that the space of continuous homomorphisms H(G, K) in the compact-open topology is a k-space whenever G is a (not necessarily commutative) metrizable topological group and K is a compact topological group which satisfies certain not too restrictive conditions.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajv-09.
	atlas-conferences.com /cgi-bin/abstract/cajv-09 (196 words)

	Eric Van Douwen's papers
		The shift on the \v Cech-Stone compactification of the integers.
		The box product of countably many metrizable spaces need not be normal.
		Along the way, he also proved that the box product of countably many metrizable spaces need not be normal, and he wrote an intriguing paper about beta X entitled "Martin's Axiom and pathological points in beta X/X".
	www.math.buffalo.edu /~sww/0papers/van_douwen_eric_k.html (2009 words)

	Pacific Journal of Mathematics - Abstract for 187-1-8 - Leonard R. Rubin and Philip J. Schapiro (Site not responding. Last check: 2007-09-25)
		Suppose that K is a simplicial complex, K is given the weak topology, and a metrizable space X is the limit of an inverse sequence of metrizable spaces X
		This latter property means that for each closed subset A of X and map f:A --> K, there exists a map F:X --> K which is an extension of f.
		As a corollary to this we get the result of Nagami that the limit of an inverse sequence of metrizable spaces each having dimension <= n has dimension <= n.
	nyjm.albany.edu:8000 /PacJ/1999/187-1-8.html (181 words)

	Does every Hausdorff space admit a metric?
		Every metric space is Hausdorff but not every Hausdorff space is metrizable!
		"Metrizable requires, in addition to Hausdorf, separability and existance of at least one countable locally finite cover.
		Those three are independent requirements; if you could do without any one of them you would have a much stronger theorem, and be famous among topologists (nobody else would notice or care)." attributed to a "DickT" on
	www.physicsforums.com /showthread.php?t=18786 (438 words)

	Agenda-040928
		Second notion -- metric spaces and metrizability Definition, examples, the metric topology,
		In order to prove Theorems 2 and 3 we will need to know about sequences, and these are quite interested by themselves:
		The sequential closure is always a subset of the closure, and in a metrizable space, they are equal.
	www.math.toronto.edu /drorbn/classes/0405/Topology/Agenda-040928/Agenda-040928.html (118 words)

	Atlas: On compact fibered spaces by J. Gerlits (Site not responding. Last check: 2007-09-25)
		An old open problem by D. Fremlin is: Is it consistent that any hereditarily Lindelöf compact T
		Tkachuk) X is metrizably fibered if it can be mapped continuously and with metrizable fibers onto a metrizable space.
		-space X is metrizably fibered iff there exist a countable cover
	atlas-conferences.com /cgi-bin/abstract/cabc-41 (162 words)

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