# Compact sets homework

nicorette

## 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.