Raaaaaawr?
So getting ready for this semester, I read a little and found the definition of a metric space. Now it seems strange that this section was skipped over in my intro analysis course, as everything we talked about in Rn is in fact just using a metric space. Then I got to thinking, well... I don't actually think I've used anything except metric spaces, ever. I know in non euclidean geometry where you can work with objects on spheres, things will get wonky and you won't have a metric space, but what is this called? Also, what else is there, if anything?