Deleted Integer Topology is First-Countable

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Corollary to Deleted Integer Topology is Second-Countable

Let $S = \R_{\ge 0} \setminus \Z$.

Let $\tau$ be the deleted integer topology on $S$.


The topological space $T = \struct {S, \tau}$ is first-countable.


Proof

From Deleted Integer Topology is Second-Countable, $T$ is second-countable.

The result follows from Second-Countable Space is First-Countable.

$\blacksquare$


Sources