Definition:Semiregular Space

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

• Definition:Separation Axioms

• 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