Definition – Interior point. – Math-reference.net

Definition

Let $A$ be a set in $\mathbb{R}$ . A point $x\in\mathbb{R}$ is referred to as an interior point of $A$ if there is a neighborhood $N(x; \epsilon)$ such that $N(x; \epsilon)\subseteq{A}$ .

The set of all interior points of $A$ is denoted by

$int ~ S$

Notes

Recall that a neighborhood of a real number is simply a set of numbers within $\epsilon$ of $x$ . So, since $\epsilon \neq 0$ and $\epsilon > 0$ , an interior point is, rather informally, a point in $A$ that is between two other points in $A$ .