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Displaying 181 – 200 of 244

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

Victor Klee, Libor Veselý, Clemente Zanco (1996)

Studia Mathematica

For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...

Semicontinuity of the Face-Function of a Covex Set

Victor Klee, Michael Martin (1971)

Commentarii mathematici Helvetici

Separation by hyperplanes in finite-dimensional vector spaces over Archimedean ordered fields.

Gritzmann, Peter, Klee, Victor (1998)

Journal of Convex Analysis

Sets invariant under projections onto one dimensional subspaces

Simon Fitzpatrick, Bruce Calvert (1991)

Commentationes Mathematicae Universitatis Carolinae

The Hahn–Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$ , and $B$ is a circled convex body in $E$ , there is a continuous linear projection $P$ onto $m$ with $P (B) \subseteq B$ . We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement.

Shilov Points and Shilov Boundaries.

Rainer Wittmann (1983)

Mathematische Annalen

Smoothness of a typical convex function

Vlastimil Klíma, Ivan Netuka (1981)

Czechoslovak Mathematical Journal

Sobre ciertas clases de conjuntos en espacios localmente convexos.

Manuel Valdivia (1980)

Collectanea Mathematica

In this paper we obtain several classes of separated locally convex spaces which are M-spaces. We give also some results on compact convex sets and new characterization of weak compactness.

Solution to a problem of S. Rolewicz

V. Montesinos (1985)

Studia Mathematica

Some characterization of locally nonconical convex sets

Witold Seredyński (2004)

Czechoslovak Mathematical Journal

A closed convex set $Q$ in a local convex topological Hausdorff spaces $X$ is called locally nonconical (LNC) if for every $x, y \in Q$ there exists an open neighbourhood $U$ of $x$ such that $(U \cap Q) + \frac{1}{2} (y - x) \subset Q$ . A set $Q$ is local cylindric (LC) if for $x, y \in Q$ , $x \neq y$ , $z \in (x, y)$ there exists an open neighbourhood $U$ of $z$ such that $U \cap Q$ (equivalently: $b d (Q) \cap U$ ) is a union of open segments parallel to $[x, y]$ . In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication $L N C \Rightarrow L C$ was proved in general, while...