space of a hypothetical basis

Question

I learned that using open balls in $\mathbb{R}^2$ as a basis would get me the standard topology. What if I use closed balls in $\mathbb{R}^2$? Do I still get a topology? I understand that if I could get one it must be different, but is it possible? Thanks

Answer 1

A point is a closed ball of radius 0, so you would get the discrete topology.