Regular Hausdorff space: Difference between revisions
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| [[Stronger than::Kolmogorov space]] || || || || {{intermediate notions short|Kolmogorov space|regular Hausdorff space}} | |||
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Revision as of 21:51, 27 January 2012
Definition
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.
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
Stronger properties
Weaker 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 |