Weakly Hausdorff space
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 is termed a weak Hausdorff space' or weakly Hausdorff space if for every compact Hausdorff space and every continouus map , the image is a closed subset of .
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 |