How to prove that something forms a base topologically speaking

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Homework Statement


If (X,d) is a metric space. I want to show that the set of all open balls and \emptyset form a base.

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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.
 
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Can you start by giving the definition of a base and the properties you need to show?
 
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