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Homework Help: How to prove that something forms a base topologically speaking

  1. Mar 2, 2014 #1
    1. The problem statement, all variables and given/known data
    If [itex](X,d)[/itex] is a metric space. I want to show that the set of all open balls and [itex]\emptyset[/itex] form a base.

    2. Relevant equations

    3. The attempt at a solution
    I know that we need to show that the union of all these sets (or balls) is the whole set. I feel like this is simple yet, I am unsure what to write so that I do not miss any important facts.
  2. jcsd
  3. Mar 2, 2014 #2
    Can you start by giving the definition of a base and the properties you need to show?
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