Regular Hausdorff space
A topological space is termed a regular Hausdorff space or a space if it satisfies the following equivalent conditions:
- It is both a regular space and a Hausdorff space.
- It is both a regular space and a T1 space.
- It is both a regular space and a Kolmogorov space (i.e., a space).
Note that outside of point-set topology, and in many elementary treatments, the term regular space is used to stand for regular 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
In the T family (properties of topological spaces related to separation axioms), this is called: T3
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|regular space|||FULL LIST, MORE INFO|
|Hausdorff space||Urysohn space|FULL LIST, MORE INFO|
|T1 space||Hausdorff space, Urysohn space|FULL LIST, MORE INFO|
|Kolmogorov space||Hausdorff space, Urysohn space|FULL LIST, MORE INFO|