An example of an infinite open cover of the interval (0,1) that has no finite subcover I've been having a hard time solving this problem that I was given in class. The problem states
" Give an example of an infinite open cover of the interval (0,1) that has no finite subcover." 
I know that the set has to be compact and that both 0 and 1 are limit points. Aside from those two known factors I'm at a complete loss as to how to go about solving this problem.

You can take the open cover $\{(0+\frac{1}{n}, 1-\frac{1}{n})\mid n>2\} $. It has no finite subcover because if it does simply take the largest $n$ and $\frac{1}{2n}$ is not included.
