How to relate interior points to a discrete metric space?

Question

I am trying to grasp the concept of metric spaces, particularly, discrete metric spaces. I would like to provide an example of interior points in a discrete metric space, but am not sure what this entails. If anyone could provide an example of interior points for any (of your choosing) discrete metric space, or proof that none exist, I would greatly appreciate the clarification!

score 2 · Accepted Answer · answered Oct 03 '16 at 16:08

2

In every discrete metric space we have that every set is both open and closed, so in particular if $E \subseteq X$ is a subset of a discrete metric space $X$, then every point in $E$ is an interior point.

answered Oct 03 '16 at 16:08

Glitch

8,331

Thanks for the explanation! :) – user3495690 Oct 03 '16 at 17:52

score 0 · Answer 2 · answered Oct 03 '16 at 16:08

0

https://en.wikipedia.org/wiki/Discrete_space

So any set is open, in particular any set is equal to its interior.

answered Oct 03 '16 at 16:08

Math.mx

1,919

How to relate interior points to a discrete metric space?

2 Answers2