tags:definition |topology |set

Boundary of a Set

Context

Statements

Definition. (@Bou95, Definition 11). Let $(X,\tau )$ be a topological space, and $S\subset X$. A point $x\in X$ is said to a boundary point of $S$ if $x$ belongs to the closure of $S$ and its complement, ie, $x\in \mathrm{cl}(S)\cap \mathrm{cl}(X\setminus S)$. The set of all boundary points is said to be the boundary of $S$.