Let . We say that is an interior point of if such that (the open ball).
In other words, is an interior point if we can form an open ball such that all of the ball is contained within .
The set of interior points of is called the interior of , written .
- is an interior point, since yields a ball that’s contained in .
- is not an interior point, since there’s no such that the resulting ball is contained in .
If , then is an open set.