Arens-Fort Space is Paracompact/Proof 2
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Theorem
Let $T = \struct {S, \tau}$ be the Arens-Fort space.
Then $T$ is a paracompact space.
Proof
We have that:
From Sequence of Implications of Separation Axioms, it follows that $T$ is a $T_3$ space.
The result follows from Lindelöf $T_3$ Space is Paracompact.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $26$. Arens-Fort Space: $5$