Category:Minkowski Functionals in Normed Vector Spaces
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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:
- $\forall x \in X: \map {p_C} x = \inf \set {t > 0 : \dfrac x t \in C}$
Subcategories
This category has only the following subcategory.
Pages in category "Minkowski Functionals in Normed Vector Spaces"
The following 4 pages are in this category, out of 4 total.
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- Minkowski Functional of Open Convex Set in Normed Vector Space is Bounded
- Minkowski Functional of Open Convex Set in Normed Vector Space is Sublinear Functional
- Minkowski Functional of Open Convex Set in Normed Vector Space is Well-Defined
- Minkowski Functional of Open Convex Set in Normed Vector Space recovers Set