Hausdorff Space

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Hausdorff space

[′hau̇s·dȯrf ‚spās]
A topological space where each pair of distinct points can be enclosed in disjoint open neighborhoods. Also known as T2 space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Hausdorff Space


in mathematics, an important type of to pological space. A Hausdorff space is a topological space wherein any two points have nonintersecting neighborhoods. Such spaces were first defined in 1914 by F. Hausdorff, who carried out a detailed study of them.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Let S and [S.sub.3] be two g[ALEPH] locally compact Hausdorff spaces. Then for any NTS [S.sub.2], the function [mathematical expression not reproducible] defined by E(f) = f(that is E(f)([A.sub.1]) ([A.sub.2]) = f ([A.sub.2], [A.sub.1]) = (f([A.sub.1])) ([A.sub.2])) for all f : [S.sub.3] x X [right arrow] [S.sub.2] is a g[ALEPH] homeomorphism.
Let X and Y be compact Hausdorff spaces, let A and B be complex-linear subspaces of C(X) and C(Y), respectively, and let p,q [member of] P.
Soft connectedness and soft Hausdorff spaces were introduced in [13].
Fuzzy Hausdorff spaces and fuzzy irresolute functions via fuzzy ideals, V Italian-Spanish Conference on General Topology and its Applications June 21-23, 2004, Almeria, Spain
We continue the study of the theory of SBT Hausdorff spaces. In order to investigate all the soft bitopological modifications of SBT Hausdorff spaces, I present new definitions of (f, [[??].sub.1] [[??].sub.2])-soft closure, SBT homeomorphism, SBT property, and hereditary SBT.
In the following section we will prove that these measures form a residual set in the space of signed Radon measures M(X) on specific Hausdorff spaces. Note that this is analogous to the density of the set of nowhere monotone functions in C([a,b]) (see [Aron et al.(2009), Theorem 3.3]).
We can see that A, B, and C are all the subset of Hausdorff spaces. With the total arrival rate constraints (8) and (9) and the total sharing probability constraint (10) in Section 3, we can reason that the sets A, B, and C are all closed.
If there are two point-fibred IFS F = {X; [f.sub.1], ..., [f.sub.N]} and G = {Y; [g.sub.1], ..., [g.sub.N]} (with common [I.sup.[infinity]]) on compact Hausdorff spaces X and Y, [A.sub.F] and [A.sub.G] being their attractors, [[pi].sub.G] the coding mapping of G, and [[tau].sub.F] the section of [[pi].sub.F], then we can define the fractal transformation (under this transformation the fractal dimension of a set could be changed) between attractors of F and G:
Joseph, On if-closed and Minimal Hausdorff Spaces, Proc.
Porter: [theta]-closed subsets of Hausdorff spaces, Pacific J.
Twenty-three papers are included, with titles that include the comparison of a Kantorovich-type and Moore theorems, related fixed point theorems for mappings and set valued mappings on two metric spaces, and some fixed point theorems in compact Hausdorff spaces. The contributors are mathematicians at universities world wide.