# Thread: Not compact by open cover

1. ## Not compact by open cover

Show that the set S = { $\frac{1}{n}$: $n \in N$ } is not compact by describing an open cover of it that does not have a finite cover.

any help appreciated!

2. Originally Posted by thaopanda
Show that the set S = { $\frac{1}{n}$: $n \in N$ } is not compact by describing an open cover of it that does not have a finite cover.
What about $O_n=\left(\frac{1}{n+1},2\right)?$

3. I don't really understand what you mean by that question...

4. Originally Posted by thaopanda
I don't really understand what you mean by that question...
Is the collect $\left\{ {O_n } \right\}$ such a cover?

5. does it have to be n+1? doesn't H = { $A_n$} where $A_n = (\frac{1}{n},2)$ work? H being the open cover with no finite subcover.