Finite Complement Topology is not Metrizable
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Theorem
Let $T = \struct {S, \tau}$ be a finite complement topology on an infinite set $S$.
Then $T$ is not a metrizable space.
Proof
We have:
$\blacksquare$
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Zariski topology