Hi

Let and be such compacts. Take one point in

For every point of there are two open sets and such that and and .

so for a finite subset of .

Now is an open set disjoint from (it is disjoint from ) which contains

Repeat that operation for every You obtain a set of open sets such that and is disjoint from (more precisely from ).

So same properties (and even better) for for a finite subset of

what can you say of and ?