Countable Complement Space is Not Weakly Countably Compact
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Theorem
Let $T = \left({S, \tau}\right)$ be a countable complement topology on an uncountable set $S$.
Then $T$ is not weakly countably compact.
Proof
From Limit Points of Countable Complement Space, if $H \subseteq S$ is countable, it contains all its limit points.
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{II}: \ 20: \ 7$
