# Set hw

1. May 3, 2008

### nicorette

1. The problem statement, all variables and given/known data

X and Y are compact sets in R^n that are disjoint. Then there must be positive distance between the elements of these sets.

2. Relevant equations

3. The attempt at a solution

since X and Y are compact , X X Y is compact. Then, for the distance function d(x in X, y in Y): R^n X R^n -> R, there is a maximum and a minimum.

I think this should be a sufficient proof, although I'm not really sure how exactly to show that X X Y is compact as well.

2. May 4, 2008

### Dick

You've got the right idea, but you haven't shown the minimum can't be zero. Have you? Do you need to show XxY is compact? Or it that something you already proved?

3. May 4, 2008

### nicorette

I don't know how to show the minimum can't be zero. So far as X x Y being compact, I just assumed, I don't know where to start for a proof

thanks a lot

4. May 4, 2008

### Dick

Don't worry about proving XxY compact for the moment, concentrate on the first one. Suppose the distance is zero. How can that be?