# Compact sets homework

## Homework Statement

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

## 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.

## Answers and Replies

Dick
Homework Helper
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?

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

Dick