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.