Condition for Open Extension Space to be T5 Space
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Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $T^*_{\bar p} = \left({S^*_p, \tau^*_{\bar p}}\right)$ be the open extension space of $T$.
Then $T^*_{\bar p}$ is a $T_5$ space iff $T$ is.
Proof
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{II}: \ 16: \ 9$
