(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Analysis Help

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