Hausdorff Space

(redirected from Hausdorff topology)

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.

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.

References in periodicals archive ?
Let S denote a locally compact semigroup; That is, a semigroup with a locally compact Hausdorff topology under which the binary operation of S is jointly continuous.
Thus the topology generated by it is a Hausdorff topology.
c) If X is metrizable, then the Hausdorff topology is always finer and, generally, strictly finer than the Fell topology.
In fact, the Hausdorff topology is the discrete-hit-and-far-miss topology (see [11]): [tau]([H.
Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc.
The family {BM (x, r, t): x [member of] X, 0 < r < 1, t > 0} is a neighborhood's system for a Hausdorff topology on X, which is called the topology induced by the generalized fuzzy metric M which is denoted by [J.
George and Veeramani [5] modified the concept of fuzzy metric space introduced by Kramosil and Michalek [10] and defined a Hausdorff topology on this fuzzy metric space.
A locally convex linear Hausdorff topology T on R is said to have property (A) if the following condition holds:
a semigroup with a locally compact Hausdorff topology whose binary operation is jointly continuous.
n]/[Gamma], one can simply appeal to a result of Fukaya [Fu1] on the equivariant Hausdorff topology.
If T is a locally m-convex Hausdorff topology on A and P the corresponding boundedness radius.
If T is a locally m-convex Hausdorff topology on A, then every open set U [subset] [beta]X contains, at least, some [x.