Talk:Deleted Integer Topology is Weakly Countably Compact

Now you've brought this up I believe that ths space may not be w.c.c after all.

Take the set $T = \left\{{n + \dfrac 1 2: n \in \Z_{\ge 0}}\right\}$. Then $S \supseteq T$ and $T$ is infinite, but any open set $\left({n .. n+1}\right) \subseteq S$ contains only one point $n + \frac 1 2 \in T$ and so $x$ is not a limit point of $T$ after all. So by definition $S$ is not w.c.c.

Please check my reasoning and we can then rewrite and so rename this page to d.i.t is not w.c.c.

My fault, I was seduced by S&S who said "[The deleted integer topology] has most of the properties of the odd-even topology". In the glossary at the back they have omitted to specify any properties for this set. --prime mover 00:34, 3 December 2011 (CST)