Hello everyone,

1) I have been banging my head against the wall trying to figure out how to prove that two subsets which are compact subsets of produce another compact subset when added together.

The problem is.. I know the definition of a compact set, but is that the right place to start? Can anyone please gently guide me in the right direction?

2) if is an open subset in Rn and V is an arbitrary subset, then U+V is open. Here I am having issues because again I know the definition of an open subset but I become paralyzed when I try to do anything with it. Frankly I'm not sure if V is an arbitrary subset of Rn but even if I assume it is, how on earth do I start?

I am still very new to proofs and I would like to learn on my own so please post only ideas of where I can or should start.

Thank you.