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
A semiregular space is a topological space satisfying the following equivalent conditions:
- The regular open subsets (these are subsets that equal the interior of their closure) form a basis for the space.
- For any and any open subset containing , there exists a regular open subset of containing and contained in .
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|regular space||regular implies semiregular||semiregular not implies regular|