Particular Point Space is not Weakly Countably Compact/Mistake

Source Work

 * Part $\text{II}$: Counterexamples
 * Section $8 - 10$: Particular Point Topology
 * Item $12$
 * Item $12$

This mistake can be seen in the second edition (1978) as republished by Dover in 1995: ISBN 0-486-68735-X

Mistake

 * [A particular point space] $X$ is not weakly countably compact since any set which does not contain $p$ has no limit points.

However, this is true only of an infinite particular point space.

By definition, a space $X$ is weakly countably compact every infinite subset of $X$ has a limit point in $X$.

But a finite particular point space has no infinite subset.

So a finite particular point space is weakly countably compact vacuously.

Also see

 * Infinite Particular Point Space is not Weakly Countably Compact