Thread: Compact in R

Hello!

I was wondering if someone could clear something up for me..

Is every non-empty, compact subset of R a closed interval in R?
It seems to me that this is true. I know that such sets are closed an bounded, but I don't know how to show that they're connected.

Any help is much appreciated!

According to the Bolzano–Weierstrass theorem, a subset of is compact if and only if it is closed and bounded. So, the union of two disjoint finite closed intervals in is compact.

Originally Posted by DrNerj

Is every non-empty, compact subset of R a closed interval in R?

is a non-empty, compact subset of

Any non-empty closed and bound subset of is compact.

Thanks a lot!
That really helped clear things up.