Show that the set S = { $\displaystyle \frac{1}{n}$: $\displaystyle n \in N$ } is not compact by describing an open cover of it that does not have a finite cover.
Show that the set S = { $\displaystyle \frac{1}{n}$: $\displaystyle n \in N$ } is not compact by describing an open cover of it that does not have a finite cover.
What about $\displaystyle O_n=\left(\frac{1}{n+1},2\right)?$
does it have to be n+1? doesn't H = {$\displaystyle A_n$} where $\displaystyle A_n = (\frac{1}{n},2)$ work? H being the open cover with no finite subcover.