Topological Interiors

Definition

Given a subset $A$ of a topological space, a point $x$ is said to be in the interior of $A$ (an interior point of) if $A$ is a neighborhood of $x$. The interior of $A$ is the set of all interior points

Notation

The interior of a set $A$ of a topological space is denoted by $\Int(A)$. Less frequently the interior is denoted by $A^\circ$¹

1. We reserve this notation for the polar of a convex set. ↩︎