Excluded Point Topology is not T3

Theorem

Let $T = \struct {S, \tau_{\bar p} }$ be a excluded point space.

Then $T$ is not a $T_3$ space.


Proof

Excluded Point Topology is Open Extension Topology of Discrete Topology
Open Extension Topology is not T3

$\blacksquare$


Sources

  • 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $13 \text { - } 15$. Excluded Point Topology: $2$
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