Odd-Even Topology is Separable

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Theorem

Let $T = \struct {\Z_{>0}, \tau}$ be a topological space where $\tau$ is the odd-even topology on the strictly positive integers $\Z_{>0}$.


Then $T$ is separable.


Proof

From Odd-Even Topology is Second-Countable, $T$ is second-countable.

The result follows from Second-Countable Space is Separable.

$\blacksquare$


Sources