Definition:Closure/Normed Vector Space

Definition

Let $M = \struct {X, \norm {\, \cdot \,} }$ be a normed vector space.

Let $S \subseteq X$.

The closure of $S$ (in $M$) is the union of $S$ and $S'$, the set of all limit points of $S$:

$S^- := S \cup S'$

Also see

• Results about set closures can be found here.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis: Chapter $1$: Normed and Banach spaces