# Homework Help: (a) If A and B are disjoint closed sets in some

1. Oct 26, 2011

### Jamin2112

(a) If A and B are disjoint closed sets in some ....

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

(a) If A and B are disjoint closed sets in some metric space X, prove that they are separated.

(b) Prove the same for disjoint open sets.

(c) Fix p in X, ∂ >0, define A to be the set of all q in Z for which d(p,q) < ∂, define B similarly, with > in place of <. Prove that A and B are separated.

2. Relevant equations

Triangle inequality, definitions of open and closed sets

3. The attempt at a solution

Give me some hints to finishing part (c).