Set compact and connected

Show that the set S := { } is compact and connected.

To show it is compact, I would need to find a finite open cover for S... I think... but I really have no idea what that means

And for it being connected, that means S cannot be written as two disjoint open sets, but again, I don't know how to prove that, since our professor only just introduced the topic....

thanks for any help you can provide! (Happy)

The Heine-Borel Theorem states that any closed and bounded set in is compact.

As for connectedness, there is a theorem that states that if you have a continuous function that maps , and is connected, then is also connected.

That should get you going in the right direction.