I'm a very beginner in topology, and I have a question.
The book I'm studying says that cofinite topologies on any infinite sets can't be induced from any metric spaces, but how do I show this?
I haven't learned anything about hausdorf, compactness, separability, or connectedness yet.
I feel that I need to use the fact that I can't make any open ball in (X,d) whose complement is finite. In here X is a set and d is a metric given.