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	Nagata–Smirnov metrization theorem - Wikipedia, the free encyclopedia
		The Nagata–Smirnov metrization theorem in topology characterizes when a topological space is metrizable.
		The theorem states that a topological space X is metrizable if and only if it is regular and Hausdorff and has a countably locally finite basis.
		Unlike the Urysohn's metrization theorem which provides a sufficient condition for metrization, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable.
	en.wikipedia.org /wiki/Nagata-Smirnov_metrization_theorem (111 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.
		Urysohn's Theorem can be restated as: A topological space is separable and metrizable if and only if it is second-countable, regular and Hausdorff.
	en.wikipedia.org /wiki/Metrization_theorems (376 words)

	Metrization theorem - Wikipedia, the free encyclopedia
		The first really useful metrization theorem was Urysohn's metrization theorem.
		(Historical note: The form of the theorem shown here was in fact proved by Tychonoff in 1926.
		The Nagata-Smirnov metrization theorem extends this to the non-separable case.
	en.wikipedia.org /wiki/Metrization_theorem (376 words)

	Search Results for theorem*
		Theorem 2 of Euclid's Phaenomena consists of four propositions with proofs for only three of them while the missing one is replaced by the remark "that this is the case has been shown elsewhere"; indeed theorem and proof are found as Theorem 10 in Autolycus's 'Rotating Sphere'.
		The theorem is then a sort of topological form of the particle-wave equivalence of quantum mechanics, and the quest for 'truly' understanding these and analogous dualities has been one of the great motivating forces in the mathematics of the last fifty years.
		Pick's theorem states that the area of a reticular polygon is L + B/2 - 1 where L is the number of reticular points inside the polygon and B is the number of reticular points on the edges of the polygon.
	www-history.mcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=theorem*&CONTEXT=1 (16744 words)

	R. H. Bing, October 20, 1914–April 28, 1986 \| By Michael Starbird \| Biographical Memoirs
		The Bing-Nagata-Smirnov metrization theorem is a fundamental result in general topology that provides a characterization of which topological spaces are generated by a metric.
		His metrization theorems hinged strongly on his understanding of a strong form of normality, and certainly one of the legacies of this paper is his definition of and initial exploration of collectionwise normality.
		This theorem was a partial result in an attempt to settle the still unresolved Poincaré conjecture in dimension 3.
	www.nap.edu /html/biomems/rbing.html (3962 words)

	PlanetMath: metrizable
		is said to be metrizable if there is a metric
		This is version 2 of metrizable, born on 2002-01-22, modified 2004-11-13.
		Object id is 1538, canonical name is Metrizable.
	planetmath.org /encyclopedia/Metrization.html (37 words)

	Metrization theorems
		A metrizable space is a topological space which is homeomorphic to a metric space.
		Metrization theorems are theorems which give sufficient conditions for a topological space to be metrizable.
		For explanations of many of the terms used in this article, the reader should see the Topology Glossary.
	www.ebroadcast.com.au /lookup/encyclopedia/me/Metrization_theorems.html (287 words)

	Description of Courses (Site not responding. Last check: 2007-11-06)
		Matching theory and its generalizations: matchings in bipartite graphs, size and structure of maximum matchings, bipartite graphs with perfect matchings, general graphs with perfect matchings, some graph-theoretical problems related to matchings, matchings and linear programming, matching algorithms, the f-factor problem, vertex packing and covering, some generalizations of matching problems.
		Lower bound and upper bound theorems for convex polytopes.
		Resolutions of the identity and the spectral theorem.
	www.cnnet.clu.edu /math/english/asunacad/descripgrad.html (847 words)

	Metrization theorem: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-06)
		Metrization theorems are theorems that give sufficient condition[for more info, click this link]s for a topological space to be metrizable.
		The Nagata-Smirnov metrization theorem (The nagata-smirnov metrization theorem in topology characterizes when a topological space is metrizable....)
		Smirnov proved that a locally metrizable Hausdorff space is metrizable if and only if it is paracompact (In mathematics, a paracompact space is a topological space in which every open cover admits an open locally...)
	www.absoluteastronomy.com /ref/metrization_theorem (1206 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		wrote: >In fact this question seems to me to be answered in many cases >by the theorem that a topological space is metrizable >if it is regular (a closed set and a point not in the set >can always be separated by disjoint open sets) >and the topology has a countable basis.
		I believe you also need to assume that the space is T1, although I don't have an counterexample offhand.
		A T1, regular, second countable topological space is metrizable (Urysohn's theorem).
	www.math.niu.edu /~rusin/papers/known-math/95/metrization (283 words)

	Topology MAT 530
		The Baire theorem states that in a complete metric space, the intersection of countably many open dense sets is dense ("dense" means that the closure is the whole space).
		To prove that some topological space is metrizable, we need to make sure that the topology on it is not too large.
		The Nagata-Smirnov metrization theorem (which we did not prove in class) gives necessary and sufficient conditions on a topological space to be metrizable.
	www.math.sunysb.edu /~azinger/mat530/fall04 (2907 words)

	Metrization theorems : search word
		A metrizable space is a topological space that is homeomorphic to a metric space.
		What Urysohn had shown, in a paper published posthumously in 1925, was the slightly weaker result that every second-countable normal Hausdorff space is metrizable.) Several other metrization theorems follow as simple corollaries to Urysohn's Theorem.
		I believed myself the more obliged to do this, because, as I was.
	www.searchword.org /me/metrization-theorems.html (424 words)

	[No title]
		The basic concepts to be introduced are: metric spaces and topology spaces, open and closed sets, continuity of functions, connectedness and compactness of topological space.
		Tychonoff theorem (chapter 3 and chapter 5, section 37)} \par}{\listtext\pard\sb99 4.
		Definition of the countability axioms and the separation axioms and Urysohn metrization theorem (chapter 4, sections 30-34)} \par}{\listtext\pard\sb99 5.
	www.math.rutgers.edu /~fluo/441/441syllabus.doc (332 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		TITLE: A domain-theoretic metrization theorem ABSTRACT: Classically, domains in the sense of Scott are used as models in the Semantics of Programming Languages.
		Concretely, the main theorem reads as follows: A topological space is metrizable iff it is modelled as a kernel of a Lebesgue measurement on a continuous poset.
		As a consequence, we gain a new understanding of the nature of classical metrization theorems from the past century.
	perso.ens-lyon.fr /pierre.lescanne/WORKSHOP_CHA_CRA_LY/waszkiewicz.txt (195 words)

	Master of science in mathematics (Site not responding. Last check: 2007-11-06)
		It discusses conformal mapping; preservation of angles, linear fractional transformation, normal families, the Riemann mapping theorem, continuity at the boundary, conformal mapping of an annulus, maximum modulus principle, Schwarz lemma, the Phragmen-Lindelof and Hadamard theorem, entire functions with rational values, and converse of maximum modulus theorem.
		Spectrum of a linear operator, study of compact operators in B(H), where H is a Hilbert space, spectral theorem for compact normal and self-adjoint operators and Fredholm alternative in Hilbert space.
		The existence theorem for ordinary differential equations, One-parameter subgroups of Lie groups, Lie algebras of vector fields on a manifold and homogeneous spaces.
	www.cuea.edu /faculties/science/masters/mscm.htm (4803 words)

	Math 240 Home Page (Driver, 03-04)
		Students are assumed to have taken at the very least a two-quarter sequence in undergraduate real analysis covering in a rigorous manner the theory of limits, continuity and the like in Euclidean spaces and general metric spaces.
		The theorems of Heine-Borel (compactness in Euclidean spaces), Bolzano-Weierstrass (existence of convergent subsequences), the theory of uniform convergence, Riemann integration theory should have been covered.
		Differentiation of measures on R^n and the fundamental theorem of calculus.
	www.math.ucsd.edu /~driver/240A-C-03-04 (609 words)

	AMCA: Classification of metrization theorems by Richard E. Hodel (Site not responding. Last check: 2007-11-06)
		We use separation axioms and infinite cardinals to classify a variety of metrization theorems.
		Of special interest is a characterization of the uniform weight u(X) of a space in terms of a condition much like the Frink Metrization Theorem.
		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/a/b/89.htm (100 words)

	Atlas: On Zero-Dimensional Images of Compact Ordered Spaces by Lutz Heindorf (Site not responding. Last check: 2007-11-06)
		exp X. Theorem 1 The space X is a continuous image of a compact ordered space iff there is a complete system \Phi of retractions for X, which is monotone, i.e.
		Theorem 2 The space X is metrizable iff there is a continuous complete system of retractions for X. Both theorems can be proved by first translating the assertions into the language of Boolean algebra.
		The if-part of Theorem 2 uses Gruenhage's metrization theorem; one establishes that X
	atlas-conferences.com /c/a/a/h/35.htm (208 words)

	Metrization theorems : Metrisable space (Site not responding. Last check: 2007-11-06)
		terms defined : Metrization theorems : Metrisable space
		All is still licensed under the GNU FDL.
		We have filed in all 50/50.html">50 states now, but these are the only ones will be made and fund raising will begin in the additional states.
	www.termsdefined.net /me/metrisable-space.html (426 words)

	Reverse Mathematics and Comprehension
		This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies
		In addition, the class of countably based MF spaces includes many topological spaces which are not metrizable.
		Remark 4 Theorem 1 shows that a certain metrization theorem is logically equivalent to
	www.math.psu.edu /simpson/papers/pi12 (1335 words)

	On the Bitopological Extension of the Bing Metrization Theorem (Site not responding. Last check: 2007-11-06)
		On the Bitopological Extension of the Bing Metrization Theorem
		Based on a Junnila's paracompactness characterization we give a definition of pairwise paracompact space which permits us to prove that a bitopological space is quasi-metrizable if, and only if, it is a pairwise paracompact space.
		An easy consequence of this result is the biquasi-metric form of the Morita metrization theorem.
	anziamj.austms.org.au /JAMSA/V44/Part2/Romaguera.html (117 words)

	[No title]
		The tangent bundle Vector bundles, transition functions Reconstruction of a vector bundle from transition functions Equivalence classes of curves and derivations; tangent vectors The tangent bundle of a manifold as a vector bundle, examples Vector fields, differential equations and flows Lie derivatives and bracket 3.
		Integration Stokes' Theorem Integration and volume on manifolds De Rham cohomology Chain and cochain complexes Homotopy theorem The degree of a map The Mayer-Vietoris theorem Typical references: Michael Spivak, A Comprehensive introduction to differential Geometry, 2nd ed., Publish or Perish, Berkeley1979; Glen Bredon, Topology and Geometry, Springer-Verlag, 1993.
		Complex integration Line integrals and Cauchy's theorem for disk and rectangle Cauchy's integral formula Cauchy's inequalities Morera's theorem, Liouville's theorem and fundamental theore= m of algebra The general form of Cauchy's theorem 5.
	www.math.sunysb.edu /graduate/syllabus (754 words)

	Research Interests (Site not responding. Last check: 2007-11-06)
		We introduce the notion of Topological Groups with the motivation of proving the special case of the Fundamental Theorem of Galois Theory where the extension is assumed to be infinite.
		We find a one to one correspondence similar to that of the standard theorem between the Closed Subgroups of the Galois Group and the Intermediate Fields of the Extension.
		We investigate our first metrization theorem which states that every second countable regular topological space is metrizable by way of Urysohn’s Lemma.
	plaza.ufl.edu /saki606/research.html (528 words)

	PlanetMath: Urysohn metrization theorem
		Cross-references: metrizable, closed, singleton, second countable, regular, topological space
		This is version 3 of Urysohn metrization theorem, born on 2002-01-22, modified 2002-05-25.
		(General topology :: Spaces with richer structures :: Metric spaces, metrizability)
	planetmath.org /encyclopedia/UrysohnMetrizationTheorem.html (58 words)

	Abstract Mathematical Obstructs (Site not responding. Last check: 2007-11-06)
		Cohen's (Tannenbaum's) proof that the Continuum (Suslin) Hypothesis is not a theorem in ZFC, and Lawvere's (Brunuel's) very short versions of the latter.
		The proof of the Tychonov Theorem after Urysohn's lemma is applied.
		The proof of the Brouwer Fixed Point Theorem not using Homotopy.
	at.yorku.ca /t/o/p/c/31.htm (382 words)

	Qualifying Exam Syllabi
		The structure theorem of finitely generated modules over a principal ideal domain as it applies to the determination of:
		Theorems; characterization of compactness for metrizable spaces, every metric space is paracompact, Tychonoff product theorem, Urysohn's lemma, metrization theorem for 2nt countable spaces
		Embedding Theorem for manifolds into Euclidean space (with proof in compact case, without proof of optimum dimension)
	www.math.ksu.edu /main/graduate/qualifying_exam_syllabi/new-qual-syllabus.html?noBorders=1 (575 words)

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