Interior (Analysis)

analysis

Definition

Interior (Analysis)

The interior $\mathring{D}\subseteq D$ of a set $D$ is the set of points for which an epsilon neighbourhood $U_{\epsilon }(x)\subseteq D$ exists.

$$\mathring{D}:=\{x\in D\mid \exists \epsilon >0:U_{\epsilon }(x)\subseteq D\}$$