Definition:Semiregular Space
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
$\struct {S, \tau}$ is a semiregular space if and only if:
- $\struct {S, \tau}$ is a Hausdorff ($T_2$) space
- The regular open sets of $T$ form a basis for $T$.
Also see
- Results about semiregular spaces can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $2$: Separation Axioms: Additional Separation Properties