tags:definition |topology |set

Topological Set Closure

Context

Statements

Definition (@Bou95, Definition 10). Let $(X,\tau )$ be a topological space, and $S\subseteq X$. The closure of $S$, denoted as $\mathrm{cl}(S)$, is the set of all elements $x\in X$ such that every topological neighborhood of $x$ meets $S$.