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Topic: Urysohn

	Urysohn biography
		After Urysohn's death, Aleksandrov argued that although Urysohn's definition of dimension was given for a metric space, it is, nevertheless, completely equivalent to the definition given by Menger for general topological spaces.
		Urysohn spotted an error in Brouwer's paper regarding a definition of dimension while he was studying it in Göttingen and easily constructed a counter-example.
		Urysohn's main contributions, in addition to the theory of dimension discussed above, are the introduction and investigation of a class of normal surfaces, metrization theorems, and an important existence theorem concerning mapping an arbitrary normed space into a
	www-groups.dcs.st-and.ac.uk /history/Biographies/Urysohn.html (1440 words)

	[No title]
		Because this theorem is part of the basic knowledge of most mathematicians, it is natural to analyze Urysohn's theorem from the point of view of Reverse Mathematics, a program in mathematical logic whose goal is to determine which set existence axioms are required to prove theorems of core mathematics.
		To analyze Urysohn's theorem, we formalize it in second-order arithmetic.
		We use this formalization to show that Urysohn's metrization theorem for countably based MF spaces is equivalent to Pi^1_2 - CA_0 over Pi^1_1 - CA_0.
	www.math.psu.edu /simpson/logic/seminar/050412.html (247 words)

	Paul Samuilovich Urysohn - Biocrawler (Site not responding. Last check: 2007-11-01)
		) (February 3, 1898 - August 17, 1924) was a Russian mathematician who is best known for his contributions in the theory of dimension, for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.
		Urysohn studied in University of Moscow from 1915 to 1921 and worked there as an assistant professor from 1921 to 1924, when he drowned while swimming off the coast of Brittany, France.
		This biographical article about a mathematician is a stub.
	www.biocrawler.com /encyclopedia/Paul_Samuilovich_Urysohn (197 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Subject: Re: regular 2nd countable spaces Date: Fri, 3 Aug 2001 16:10:11 -0500 Newsgroups: sci.math I am accustomed to T_2.5 meaning completely Hausdorff or Urysohn in the stronger sense, viz., for any two points p != q there is a continuous function into [0,1] with f(p) = 0 and f(q) = 1.
		(But I've also seen 'Urysohn space' used in > > a stronger sense.) > I am accustomed to T_2.5 meaning completely Hausdorff or Urysohn in the > stronger sense, viz., for any two points p != q there is a continuous > function into [0,1] with f(p) = 0 and f(q) = 1.
		Yes, I think I got 'completely Hausdorff' and 'Urysohn' mixed up - 'Urysohn' is usually used in the weaker sense and 'completely Hausdorff' in the stronger sense (although I've seen them the other way around too).
	www.math.niu.edu /~rusin/known-math/01_incoming/T_n (430 words)

	Urysohn's Lemma (Site not responding. Last check: 2007-11-01)
		Urysohn (biography) developed an equivalent criterion for a normal space.
		We present the criterion first, then prove it is equivalent to the original definition.
		We can use Urysohn's lemma to build a continuous function on s that is 0 on e and 1 on f.
	www.mathreference.com /top,ury.html (488 words)

	AMCA: Countable connected Hausdorff and Urysohn bunches of arcs in the plane by Piotr Minc (Site not responding. Last check: 2007-11-01)
		We answer a question by Krasinkiewicz, Re\'nska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane.
		We observe that if a graph G cannot be embedded in the plane, then any generalized graph modeled on G is not embeddable in the plane.
		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/p/c/40.htm (167 words)

	Workshop on the Urysohn Space
		The Urysohn space U is the universal complete metric separable space.
		An interesting approach to the Urysohn space was proposed by A.
		At this stage, we hope to be able to cover the cost of local expenses of all participants for the
	www.math.bgu.ac.il /~arkady/Workshop_2006/main_page.html (333 words)

	Atlas: Group of isometries and dynamics on the Urysohn space by Anatoly M. Vershik (Site not responding. Last check: 2007-11-01)
		Among several aspects of the theory of universal Urysohn space one of the main is the investigation of the group of its isometries.
		Cameron and speaker about the existence of the structure of the monothetic abelian group in the Urysohn space; this made the Urysohn space as the torus of the continuous dimension.
		Finally, the theory of measures on the Urysohn space can be developed on the base of the theory of the random matrices of the special type.
	atlas-conferences.com /cgi-bin/abstract/cask-12 (251 words)

	RFSCDME Sweet 16 Match #1 - Urysohn (6) at Pillow (2) - Actuarial Outpost
		Urysohn (6) - After dealing an early crushing blow to Gomer in round 1, Urysohn proved not to be a one time wonder with a sound thrashing of Moe.
		Some have argued that Urysohn's road to the Sweet 16 has been too easy.
		But Urysohn asked directly, and Pillow through a proxy (or maybe the proxy acted on his own?) and Urysohn asked first, and besides, his spam was funnier.
	www.actuarialoutpost.com /actuarial_discussion_forum/showthread.php?t=51555 (1263 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		In Part 1 of this talk, I defined MF spaces and showed that Urysohn's theorem for MF spaces implies Pi^1_2 - CA_0 over Pi^1_1 - CA_0.
		In Part 2, I will sketch the proof that Urysohn's theorem for MF spaces is provable in Pi^1_2 - CA_0.
		I will also show that several statements which are classically equivalent to Urysohn's theorem for MF spaces are also equivalent to Pi^1_2 - CA_0 over Pi^1_1 - CA_0.
	www.math.psu.edu /simpson/logic/seminar/050419.html (146 words)

	The Urysohn Lemma
		This article is the third part of a paper proving the fundamental Urysohn Theorem concerning the existence of a real valued continuous function on a normal topological space.
		In the first part, we describe the construction of the function solving thesis of the Urysohn Lemma.
		The second part contains the proof of the Urysohn Lemma in normal space and the proof of the same theorem for compact space.
	www.mizar.org /JFM/Vol13/urysohn3.html (147 words)

	Urysohn's Lemma -- from Wolfram MathWorld
		with this property is called a Urysohn function.
		This formulation refers to the definition of normal space given by Kelley (1955, p.
		Joshi, K. "The Urysohn Characterization of Normality." §7.3 in
	mathworld.wolfram.com /UrysohnsLemma.html (99 words)

	abstract (Site not responding. Last check: 2007-11-01)
		A topological space X is continuously Urysohn if for each pair of distinct points x,y in X there is a continuous real-valued function f
		We show that spaces with this property are precisely the spaces that have a weaker metric topology.
		We show that a continuously Urysohn space may fail to be strongly separating.
	www.iam.unibe.ch /~halbeis/publications/urysohn_abs.html (185 words)

	Citebase - Distance matrices, random metrics and Urysohn space (Site not responding. Last check: 2007-11-01)
		Authors: Vershik, A. We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry.
		It happened that the generic Polish spaces in this sense of this universum is so called Urysohn spaces defined by P.S.Urysohn in 20-th, and generic metric triple (= metric space with probability borel measure) is also Urysohn space with non-degenerated measure.
		We prove that the complete invariant of the metric space with measure up to measure preserving isometries is so called matrix distribution - invarinat and ergodic measure with respect to infinite symmetric group which is concentrated on the cone of distance matrices.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0203008 (187 words)

	CiteULike: Tag urysohn (Site not responding. Last check: 2007-11-01)
		The isometry group of the Urysohn space as a Levy group
		Extension theorems and reconstruction theorems for the Urysohn Universal Space
		posted to metric-geometry metric-space random-matrix urysohn vershik by ansobol as
	www.citeulike.org /tag/urysohn (63 words)

	On continuously Urysohn and strongly separating spaces (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		On continuously Urysohn and strongly separating spaces (2000)
		Abstract: A topological space X is continuously Urysohn if for each pair of distinct points x; y 2 X there is a continuous real-valued function f x;y 2 C(X) such that f x;y (x) 6= f x;y (y) and the correspondence (x; y) !
		Metric spaces are examples of continuously Urysohn spaces with the additional property that the functions f x;y depend on just one parameter.
	citeseer.ist.psu.edu /halbeisen00continuously.html (335 words)

	I P M - Bulletin Board
		Erdos and Renyi showed that there is a unique countable random graph (up to isomorphism).
		Earlier, Urysohn had constructed a Polish space (a complete separable metric space) with similar homogeneity and universality properties.
		It took longer for mathematicians to become interested in this space; but there are now some results on its isometry group.
	www.ipm.ac.ir /IPM/news/ViewNewsInfo.jsp?NTID=138 (390 words)

	Atlas: Workshop on the universal Urysohn metric space - List of Speakers
		Julien Melleray Two methods to study the geometric properties of the Urysohn space and the structure of its isometry group
		Vladimir Pestov Approximation of the isometry group of the Urysohn space with finite subgroups
		Matatyahu Rubin Extension theorems and reconstruction theorems for the universal Urysohn Space II Norbert Sauer Metric spaces as binary relational structures
	atlas-conferences.com /cgi-bin/abstract/cask-01 (288 words)

	Workshop on the Urysohn Space
		of the Urysohn space with finite subgroups.
		Talk: Group of isometries and dynamics on the Urysohn space.
		There could well be changes to this list.
	www.math.bgu.ac.il /~arkady/Workshop_2006/abstracts.html (296 words)

	Urysohn Lemma
		as my first two closed sets, and use the Urysohn lemma to define a continuous function from X to [1/2, 1] choosing
		as my closed sets, and use the Urysohn lemma to find a function from X to [1/3, 1/2] choosing
		In case it's not clear, I essentially plan on applying the Urysohn lemma infinitely many times, and the k
	www.physicsforums.com /showthread.php?threadid=104368 (1179 words)

	Some isometry groups of Urysohn space (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Abstract: We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.
		0.2: On continuously Urysohn and strongly separating spaces - Halbeisen, Hungerbühler (2000)
	citeseer.ist.psu.edu /701834.html (239 words)

	RFSCDME Round 2, Match 5: Moe (14) at Urysohn (6) - Actuarial Outpost
		When he isn't busy filming the last season of Everybody Loves Raymond, Ray Romano enjoys imitating a Simpsons' bartender over in Political.
		In an effort to take votes away from Urysohn's base supporters (the ban tim>< alliance), Moe promises to do his best to contain tim>< to The Reef.
		For those thinking of not voting for Moe, be very wary.
	www.actuary.ca /actuarial_discussion_forum/showthread.php?t=49877 (1119 words)

	University of Oklahoma course: Math 5863, Intro to Topology II, Spring 2004
		During the first few weeks of the semester we will be discussing the following topics:
		Class 1: Urysohn Lemma and Tietsze Extension Theorem
		A good reference for all of this material is Munkre's book.
	www.math.ou.edu /~amiller/5863/index.html (385 words)

	Citebase - Geometry in Urysohn's universal metric space (Site not responding. Last check: 2007-11-01)
		Citebase - Geometry in Urysohn's universal metric space
		Recently, much interest was devoted to the Urysohn universal metric space U and its isometries; this paper is a contribution to this field of research.
		We also answer in the negative a question of Clemens, proving that any Polish metric space is isometric to the set of fixed points of some isometry of U. Comment: v2: corrected some grammatical errors and typos, and added a part dealing with properties of the sets of fixed points of isometries
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0505508 (138 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-11-01)
		math.RT/0601700 Representations of residually finite groups by isometries of the Urysohn space.
		math.GN/0509402 The isometry group of the Urysohn space as a Levy group.
		math.FA/0407444 Oscillation stability of the Urysohn metric space.
	front.math.ucdavis.edu /author/Pestov-V* (372 words)

	Connected Urysohn subtopologies by Richard G. Wilson (Site not responding. Last check: 2007-11-01)
		We show that each second countable Urysohn space which is not Urysohn-closed can be condensed onto a connected Urysohn space and as a corollary we characterize those countable Urysohn spaces which have connected Urysohn subtopologies.
		We also answer two questions from [Tkachuk and Wilson, Weaker connected Hausdorff topologies for spaces with a countable network] regarding condensations onto connected Hausdorff spaces.
		Keywords: Second countable connected Urysohn space, countable network, condensation, Urysohn family, Urysohn filter, Urysohn-closed space
	at.yorku.ca /b/a/a/m/05.htm (85 words)

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