Countable Fort Space is Metrizable
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Theorem
Let $T = \struct {S, \tau_p}$ be a Fort space on a countably infinite set $S$.
Then $T$ is a metrizable space.
Proof
We have:
The result follows from Urysohn's Metrization Theorem.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $23$. Countable Fort Space: $6$