Open sets and sets of interior points
Need verification of a proof please
Let be the set of all interior points of a set .
Prove is always open
Consider . a neighborhood of such that
This is an open set, so a neighborhood of so
So consists of interior points of , so is open.
Proof correct? Any alternatives or ways to make it cleaner/more elegant?
Re: Open sets and sets of interior points
It is correct. Basically you are noting that a neighborhood is a neighborhood of each of its points.
Originally Posted by I-Think