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Homework Help: Analysis Help

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Let (X,d) be a metric space and let A be a non-empty subset of X. Prove that A is open if and only if it can be written as the union of a family of open balls of the form Br(x) = {y ∈ X|d(x,y) < r} (the radius r may depend on the point x).

    2. Relevant equations

    3. The attempt at a solution
    I have no idea where to start with this.
  2. jcsd
  3. Jan 19, 2010 #2


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    Science Advisor
    Homework Helper

    What's the definition of an open set in a metric space? Is the union of open sets open? If you look these things up, it will help you a lot.
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