I am looking for some examples / definitions of these concepts so I can better understand other ones.

Namely, I am looking for all four permutations:

1. Unbounded and closed
2. Unbounded and open
3. Bound and closed.
4. Bound and open.

Apparently this is also related to the concept of "compactness" but "every open cover of the space has a finite subcover" doesn't mean anything to me.

Seeing some examples and understanding how these are defined would be helpful (I am trying to eventually understand the intuition behind the proof of Extreme Value Theorem but I need to understand these concepts first).