Definition:Absolutely Convex Set

Definition

Let $\Bbb F \in \set {\R, \C}$.

Let $X$ be a vector space over $\Bbb F$.

Let $A \subseteq X$.

We say that $A$ is absolutely convex if and only if:

$A$ is convex and balanced.

Sources

• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $2.1$: Normed Spaces