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.
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.