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Acute triangles are defined by having all angles less than $π / 2$ , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension $n \geq 3$ , acuteness is defined by demanding that all dihedral angles between $(n - 1)$ -dimensional faces are smaller than $π / 2$ . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property of acuteness...

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...

Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi (1999)

Studia Mathematica

An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_{X} (e)$ from e to X has fixed cardinality n+1 ( $n \subseteq ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_{X} (e)$ from e to X where X is a compact subset of .

Some intersection and generation properties of convex sets

Robert E. Jamison (1977)

Compositio Mathematica

Some results on groups with unique square roots

Moskowitz, Martin A. (1974)

Portugaliae mathematica

Split Faces and Projective Sets in a Metrizable Compact Convex Set.

P.J. Spacey (1976)

Mathematische Annalen

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

Azé, D., Lucchetti, R. (1996)

Serdica Mathematical Journal

* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of its conjugate...

Starshapedness in convexity spaces

Krzysztof Kołodziejczyk (1985)

Compositio Mathematica

Stufenkonvexität in der Geometrie

KÁROLY BEZDEK, István Joó (1985)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Sublinear Functions on R.

Edgar Berz (1975)

Aequationes mathematicae

Suites décroissantes de simplexes

David A. Edwards (1973/1974)

Séminaire Choquet. Initiation à l'analyse

Sur la frontière d'un convexe mobile

Manuel D.P. Monteiro Marques (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Siano $A$ , $B$ sottoinsiemi convessi, chiusi e limitati di uno spazio normato $X$ , con le frontiere $f r A$ , $f r B$ . Dimostriamo che $h(A,B)=h(frA,frB)$ , dove $h$ è la metrica di Hausdorff tra sottoinsiemi chiusi di $X$ . Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».

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Séparation forte $k$ -branlante de deux convexes

Separation of two convex sets by operators

Sets of constant width and diametrically complete setes in normed spaces

Simplices rarely contain their circumcenter in high dimensions