Countable Excluded Point Space is Second-Countable/Proof 2
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Theorem
Let $T = \struct {S, \tau_{\bar p} }$ be a countable excluded point space.
Then $T$ is a second-countable space.
Proof
We have:
- Countable Discrete Space is Second-Countable
- Excluded Point Topology is Open Extension Topology of Discrete Topology
The result follows from Condition for Open Extension Space to be Second-Countable.
$\blacksquare$