Definition – Boundary point. – Math-reference.net

Definition

Let $A$ be a set in $\mathbb{R}$ . A point $x\in A$ is referred to as a boundry point of $A$ if, for every single neighborhood of $x$ , $N(x; \epsilon)$ , the following is true,

$N(x; \epsilon) \cap A \neq \emptyset$ and $N(x; \epsilon) \cap (\mathbb{R}\setminus{A}) \neq \emptyset$

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

$bd~ A$

Notes