Category:Minkowski Functionals in Normed Vector Spaces

This category contains results about Minkowski functionals in normed vector spaces.

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

Let $\struct {X, \norm \cdot}$ be a normed vector space over $\Bbb F$.

Let $C$ be an open convex subset of $X$ with $0 \in C$.

The Minkowski functional of $C$ is the mapping $p_C : X \to \hointr 0 \infty$ defined as:

$\forall x \in X: \map {p_C} x = \inf \set {t > 0 : \dfrac x t \in C}$