Definition:Perfectly T4 Space
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
$T$ is a perfectly $T_4$ space if and only if:
- $(1): \quad T$ is a $T_4$ space
- $(2): \quad$ Every closed set in $T$ is a $G_\delta$ set.
That is:
- Every closed set in $T$ can be written as a countable intersection of open sets of $T$.
Also see
- Results about perfectly $T_4$ 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