# How to prove that something forms a base topologically speaking

1. Mar 2, 2014

### snesnerd

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

### micromass

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