# Compact Complement Topology is Second-Countable

## Theorem

Let $T = \left({\R, \tau}\right)$ be the compact complement topology on $\R$.

Then $T$ is a second-countable space.

## Proof

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{II}: \ 22: \ 5$