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 It might be outdated or ideologically biased.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 ?
[S.sub.1] is said to be g[ALEPH] Hausdorff space or [T.sub.2] space if for any two [ALEPH]--sets A and B with A [intersection] B = [0.sub.~],there exist g[ALEPH] open sets U and V, such that A [??] U,B [??] V and U [intersection] V = [0.sub.~].
In [2], a result (Theorem 1 on page 27) is given describing the density of a subset of C(X,K)[cross product]Y in C(X,Y) for a Tikhonov space X and topological linear Hausdorff space Y over K (again in the compact-open topology).
P.Nanzetta and D Plank [7] extended some characterization to an arbitrary completely regular Hausdorff space X and derived some corollaries.
Let S = ([s.sub.n]) be a sequence of self-maps on a Hausdorff space X.
Let Xbea compact Hausdorff space, let G be a finite group acting freely on [S.sup.n] and let H be a cyclic subgroup of G of order prime p.
Let X be a convex space and Y a Hausdorff space. More early in 1997 [19], we introduced a 'better' admissible class B of multimaps as follows:
It follows that the spectrum [bar.S] of A is a compact Hausdorff space. Furthermore, since points of S determine complex homomorphisms of A, there is a continuous map [alpha] : S [right arrow] [bar.S], with dense image, such that f [??] fo[alpha] : C([bar.S]) [right arrow] A is an isometric isomorphism of C([bar.S]) onto A, when [alpha] is injective.
Aldrich (2014) offers an example in topology with the statement: "A compact Hausdorff space is normal".
A New Form of Fuzzy Hausdorff Space and Related Topics via Fuzzy Idealization, IOSR Journal of Mathematics (IOSR-JM), Volume 3, Issue 5 (Sep.-Oct.
In this paper, I present the definition of soft bitopological Hausdorff space and construct some basic properties.
If X is an [A]-[theta]-paracompact Hausdorff space, then it is [A]-[theta]-regular.