Is the sum of two compact subsets of Rn compact + another problem

Hello everyone,

1) I have been banging my head against the wall trying to figure out how to prove that two subsets $\displaystyle A, B$ which are compact subsets of $\displaystyle R^n$ 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 $\displaystyle U$ 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.

Re: Is the sum of two compact subsets of Rn compact + another problem

take two sets A and B then define f(x,y)=x+y, x belongs to A and y belongs to B, f is continuous, continuous image of compact is compact. done