Math Help - Set compact and connected

1. Set compact and connected

Show that the set S := { $(x,y) \in R^2 : x^2 + y^2 = 1$} 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!

2. The Heine-Borel Theorem states that any closed and bounded set in $\mathbb{R}^n$ is compact.

As for connectedness, there is a theorem that states that if you have a continuous function $f$ that maps $E\subset X\longrightarrow Y$, and $E$ is connected, then $f(E)$ is also connected.

That should get you going in the right direction.