- #1

- 4

- 0

## 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.

## Homework Equations

## 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.