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

  1. Oct 26, 2011 #1
    (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).

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  2. jcsd
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