Particular Point Space is Pseudocompact

Theorem

Let $T = \struct {S, \tau_p}$ be a particular point space.


Then $T$ is pseudocompact.


Proof

We have that:

a Particular Point Space is Irreducible
an Irreducible Space is Pseudocompact.

$\blacksquare$


Sources

  • 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $8 \text { - } 10$. Particular Point Topology: $12$
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