Compact Complement Topology is Second-Countable
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Theorem
Let $T = \struct {\R, \tau}$ be the compact complement topology on $\R$.
Then $T$ is a second-countable space.
Proof
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Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $22$. Compact Complement Topology: $5$