In the textbook I am working with, an isolated point of A is defined to be a point X in A such that there exists a neighborhood (open ε-ball) centered on X containing no point in A other than X itself.(adsbygoogle = window.adsbygoogle || []).push({});

A boundary point of A (which need not be in A) is defined as a point X in A such that every open ε-ball centered on X contains at least one point in A and at least one point not in A.

Is it the case that isolated points must be boundary points? Most textbooks use definitions other than the one I'm using, hence I am very confused.

Also, maybe this is true for metric spaces but not for topological spaces?

BiP

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Isolated points must be boundary points?

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**