6
$\begingroup$

I was wondering what can be said about the interior of $\{{4}\}$, the empty set?

The interior of a set $A$ is the largest open set contained by $A$. Hence, if the set at hand is a singleton, then isn't the interior of the singleton the empty set?

  • 7
    it sounds like you're talking about $\mathbb{R}$ with the standard topology, right? You should specify. There are definitely contexts where the interior of a singleton is the singleton itself, such as in any discrete space2012-11-12

3 Answers 3