
	Where results make sense

Topic: Regular Hausdorff space

Related Topics

Hausdorff space

Hausdorff dimension

Felix Hausdorff

Hausdorff paradox

Campbell Hausdorff formula

Gromov Hausdorff convergence

Hausdorff distance

Regular Hausdorff

normal Hausdorff

Hausdorff topologies

Completely Hausdorff space

Paracompact Hausdorff space

In the News (Sun 12 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Regular space
		X is a regular space iff, given any closed set F and any point x that does not belong to F, there are a neighbourhood U of x and a neighbourhood V of F that are disjoint.
		(Hausdorffness); all are equivalent in the context of regular spaces.
		On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems.
	www.ebroadcast.com.au /lookup/encyclopedia/t3/T3_space.html (917 words)

	PlanetMath: paracompact topological space
		Any metric or metrizable space is paracompact (A. Stone).
		Cross-references: pseudometric space, compact, regular, Hausdorff space, cover, partition of unity, metrizable space, metric, properties, open subsets, open refinement, locally finite, open cover, topological space
		This is version 5 of paracompact topological space, born on 2002-01-22, modified 2007-06-24.
	planetmath.org /encyclopedia/Paracompact.html (82 words)

	Closed set
		In a first countable space (such as a metric space), it is enough to consider only sequences, instead of all nets.
		However, the compact Hausdorff spaces are "absolutely closed" in a certain sense.
		Stone-Čech compactification, a process that turns a completely regular Hausdorff space into a compact Hausdorff space, may be described as adjoining limits of certain nonconvergent nets to the space.
	www.ebroadcast.com.au /lookup/encyclopedia/cl/Closed_set.html (451 words)

	Reference.com/Encyclopedia/Regular space
		Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition.
		space that is not Hausdorff (and hence not preregular) cannot be regular.
		Suppose that A is a set in a topological space X and f is a continuous function from A to some space Y.
	www.reference.com /browse/wiki/Regular_space (1001 words)

	Regular space - Wikipedia, the free encyclopedia
		spaces are particularly convenient kinds of topological spaces.
		X is a regular space if and only if, given any closed set F and any point x that does not belong to F, there exists a neighbourhood U of x and a neighbourhood V of F that are disjoint.
		Suppose that A is a set in a topological space X and f is a continuous function from A to some space Y.
	en.wikipedia.org /wiki/Regular_space (963 words)

	PlanetMath: T0 space
		space is the Sierpinski space, which is not
		See Also: ball, T1 space, Hausdorff space, regular space, T3 space
		This is version 8 of T0 space, born on 2002-02-08, modified 2002-02-09.
	planetmath.org /encyclopedia/T0Space.html (57 words)

	Glossary of Terms
		The system is said to be a Ergodic when the time averages (the average of time intervals) are the same as the control space averages, where the control space average is weighted by the probability that the trajectory visits a particular portion of the control space.
		Hausdorff dimension: To define the d-dimensional volume of a sharp point for an arbitrary, non-integer d the Hausdorff dimension of the space is the value for which the d-dimension volume changes from infinity to zero.
		Hyperbolic point: A point in phase space which is bisected by a pair of separatrixes whereby it is stable along one and unstable along the other.
	www.sun.rhbnc.ac.uk /~uhap045/316/glossyaaj.html (1475 words)

	Closing Resource Center - closing time semisonic
		In a first-countable self closing gates space (such as a closing the achievement gap metric space), it is enough closing astroworld closing gifts to consider only sequences, instead of all nets.
		However, the compact Hausdorff spaces are closing costs "absolutely real estate closing closing programs closed" in a certain sense.
		Stone- ech compactification, a process that turns a completely regular Hausdorff space into a compact Hausdorff space, may be described as adjoining limits of certain nonconvergent nets to the space.
	www.taxgloss.com /Tax-Real_Estate_Topics_A_-_I-/Closing.html (676 words)

	Topology MAT 530
		The next were the formal definitions of metric and topological spaces, bases and subbases in topological spaces (i.e., a description of different ways to define topology on a set).
		A continuous invertible map from a compact space to a Hausdorff space is a homeomeorphism.
		The Urysohn lemma states that for a normal topological space X and two disjoint closed subsets A and B of it, there exists a continuous function from X to [0,1] that is 0 on A and 1 on B.
	www.math.sunysb.edu /~azinger/mat530/fall04/index.htm (2907 words)

	FAH Excerpt: Separation
		space, and every preregular space is also a symmetric space.
		space'', and ``completely regular Hausdorff space'' are used interchangeably in the literature; they all describe the same thing.
		This book considers the non-Hausdorff case as well, because one of the best ways to describe a weak topology on a topological vector space (generally Hausdorff, in applications) is as the supremum of a collection of pseudometric topologies (each of which is not Hausdorff).
	www.math.vanderbilt.edu /~schectex/ccc/excerpts/separat.html (481 words)

	Springer Online Reference Works
		The importance of compact-open topologies is due to the fact that they are essential elements in Pontryagin's theory of duality of locally compact commutative groups and participate in the construction of skew products.
		is a Hausdorff space, the compact-open topology also satisfies the Hausdorff separation axiom.
		The group of homeomorphisms of an arbitrary locally compact Hausdorff space into itself need not be a topological group with respect to the compact-open topology (the transition to the inverse element may prove to be a discontinuous mapping with respect to this topology), but if a locally compact Hausdorff space
	eom.springer.de /c/c023500.htm (316 words)

	Topology glossary - Wikipedia, the free encyclopedia
		A partition of unity of a space X is a set of continuous functions from X to [0, 1] such that any point has a neighbourhood where all but a finite number of the functions are identically zero, and the sum of all the functions on the entire space is identically 1.
		A pseudometric space (M, d) is a set M equipped with a function d : M × M → R satisfying all the conditions of a metric space, except possibly the identity of indiscernibles.
		A space is regular if, whenever C is a closed set and x is a point not in C, then C and x have disjoint neighbourhoods.
	en.wikipedia.org /wiki/Topology_glossary (4707 words)

	[No title]
		The question whether there always exists a compatible nontransitive totally bounded quasi-uniformity for infinite "nice" spaces originated when the second and third authors were working on problems related to the semilattice of totally bounded quasi-uniformities that a topological space admits [KL2].
		To see this, recall for instance that each compact Hausdorff space admits a unique uniformity, which is transitive if and only if the space is (strongly) zero-dimensional.
		So even the problem whether each infinite compact zero-dimensional Hausdorff space admits a nontransitive totally bounded quasi-uniformity is nontrivial and its positive solution evidently needs a truely nonsymmetric approach.
	at.yorku.ca /i/a/a/i/03.htm (622 words)

	Algebraic geometry Summary
		Regular functions on affine n-space are thus exactly the same as polynomials over k in n variables.
		Just as continuous functions are the natural maps on topological spaces and smooth functions are the natural maps on differentiable manifolds, there is a natural class of functions on an algebraic set, called regular functions.
		It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal topological space, where the Tietze extension theorem guarantees that a continuous function on a closed subset always extends to the ambient topological space.
	www.bookrags.com /Algebraic_geometry (2571 words)

	Completely Hausdorff space - Wikipedia, the free encyclopedia
		In topology, completely Hausdorff spaces and Urysohn spaces are types of topological spaces satisfying slightly stronger separation axioms than the more familiar Hausdorff space.
		A completely Hausdorff space, or functionally Hausdorff space, is a space in which any two distinct points can be separated by a function.
		There are obscure examples of spaces which are Hausdorff but not Urysohn, and spaces which are Urysohn but not completely Hausdorff or regular Hausdorff.
	en.wikipedia.org /wiki/Completely_Hausdorff_space (459 words)

	Algebraic Topology: Two-dimensional manifolds
		An n-dimensional manifold is a Hausdorff space that is locally isomorphic to Euclidean n-space E(n).
		This is a covering of the space with finitely many triangles, homeomorphic images of an ordinary plane triangle, where two triangles either are disjoint, or have a point or an edge in common, each edge is in precisely two triangles, and the residue at a point is a polygon.
		An n-dimensional manifold with boundary is a Hausdorff space where each point has a neighbourhood isomorphic to an open set in a closed halfspace in Euclidean n-space E(n).
	www.win.tue.nl /~aeb/at/algtop-4.html (985 words)

	[No title]
		A space X is completely regular if for any point x 2 X and any closed set A X not containing x, there exists f 2 C(X) such that f(x) = 0 and f(A) = 1, i.e., real valued functions separate points from closed sets.
		It is not hard to see that that a regular space in which every point has a Tychonoff neighborhood is already a Tychonoff space.
		When H is a p-group, it is a consequence of Miller's version of the Sullivan conjecture that the homotopy fixed point space of (H)(n), that is, Hom H (EH; (H)(n)) is homotopy equivalent to the fixed point space of (H)(n)[[1], Theorem A].
	hopf.math.purdue.edu /Feldman-Wilce/fibdegen.txt (5513 words)

	Verizon Dsl Service
		As it turns out, uniform spaces, Cauchy spaces, are always R0, so the terminology is consistent.) (A completely regular T0 space.
		As it turns out, uniform spaces, Cauchy spaces, are always R0, so the resulting space is preferred).
		An F set; is a metric space is regular Hausdorff.
	t1.2vv1.com /verizondslservice.html (132 words)

	AMCA: Spaces in which Point-finite Open Covers have Finite Subcovers by Nurettin Ergun
		Another related well known result has been proved by Iseki and Kasahara in 1957: A regular Hausdorff space X is countably compact if and only if every point-finite open cover of X has a finite subcover.
		He defined a non countably compact Hausdorff space in which point-finite open covers have finite subcovers.
		In fact any countably compact Hausdorff space is collectionwise Hausdorff since closed-discrete subsets are necessarily finite in such spaces, but, examples of non-regular countably compact Hausdorff spaces are already known.
	at.yorku.ca /c/a/e/h/05.htm (519 words)

	Separation axioms
		In a Hausdorff space, distinct points are "housed off" from one another by open sets.
		It follows that every finite set is closed in a Hausdorff space and the topology is therefore stronger than the cofinite topology.
		space with a countable basis is metrisable (that is, the topology may be obtained from a metric).
	www-groups.dcs.st-and.ac.uk /~john/MT4522/Lectures/L18.html (481 words)

	m425
		Topics include metric spaces, topological spaces, continuous functions, connectedness, compactness, countability and separation axioms, the fundamental group, and the classification of surfaces.
		All subsets of a metric space are either open or closed.
		Prove that the limit of a convergent sequence is unique in a Hausdorff space.
	ac.marywood.edu /johnsonc/www/m425.htm (770 words)

	Separation Axioms (Site not responding. Last check: 2007-10-26)
		Hausdorff (biography) developed criteria that describe the "connectedness" of a topology.
		Thus every space can be crunched down to a space that is half Hausdorff.
		We're getting a head of ourselves, but let's say you know what a metric space is. Let g and h be disjoint closed sets in a metric space.
	www.mathreference.com /top,sep.html (484 words)

	Roitman Proceedings Abstract (Site not responding. Last check: 2007-10-26)
		A space is found, for any α, which has spread α and which is not the set-theoretic union of a hereditarily α-Lindelof and a hereditarily α-separable space.
		At the 1972 Bolyai Janos Mathematical Society Colloquium, A. Hajnal and I. Juhasz noted that every known Hausdorff space of spread ω was the union of a hereditary separable space and a hereditarily Lindelof space.
		The main result of this paper is a family of counterexamples to a generalization of this situation; the method of proof will also yield, in Lemma 2(c), a family of spaces such that no "large" subspaces are regular.
	www.agnesscott.edu /lriddle/women/abstracts/roitman_abstract1.htm (109 words)

	Compact and Hausdorff
		An important corollary is that a continuous map of a compact space into a hausdorff space is bicontinuous.
		If a continuous function is invertible, and maps a compact space onto a hausdorff space, the map is bicontinuous, and implements a homeomorphism.
		We already showed that a map from a compact space onto a hausdorff space is a homeomorphism, and that isn't the case here; hence the domain of f is not compact.
	www.mathreference.com /top-cs,haus.html (693 words)

	Orðasafn: H
		Hausdorff maximal principle hákeðjulögmál Hausdorffs, = maximal chain principle.
		Hausdorff separation axiom aðgreiningareiginleiki Hausdorffs, frumsenda Hausdorffs, frumsetning Hausdorffs.
		4 (of a space with group action) einsleitur.
	www.hi.is /~mmh/ord/safn/safnH.html (858 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		BX is compact Hausdorff, of course, and B is a functor from spaces to compact Hausdorff spaces.
		X is a subspace of a completely regular space c.
		X is a subspace of a compact Hausdorff space Note that regularity and complete regularity are (obviously) inherited by subspaces, but normality is not.
	www.lehigh.edu /dmd1/public/www-data/tg1013.txt (486 words)

	Letter B
		A nonempty metric space (PL) cannot be a,I>union (PL) of countable (PL) family of nowhere dense spaces (PL).
		A pointwise-bounded (PL) family of continuous (PL) linear operators (PL) from a Banach space (PL) to a normed space (PL) is uniformly bounded.
		The number of base vectors is the dimension of the vector space and may be infinite.
	members.fortunecity.com /jonhays/letterB.htm (1785 words)

Try your search on: Qwika (all wikis)