Weakly Hausdorff space

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This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A topological space X is termed a weak Hausdorff space' or weakly Hausdorff space if for every compact Hausdorff space K and every continouus map f:K \to X, the image f(K) is a closed subset of X.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Hausdorff space any two distinct points are separated by disjoint open subsets |FULL LIST, MORE INFO
KC-space every compact subset of the space is closed |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
US-space every sequence of points in the space has at most one limit KC-space|FULL LIST, MORE INFO
T1 space every singleton subset is closed KC-space|FULL LIST, MORE INFO