On some criteria of convexity for compact sets
type: Item
instance of: scholarly article
title: On some criteria of convexity for compact sets
zbMATH Open document ID: 1246.52010
author: Yu. B. Zelinskyj
author: I. Yu. Vyhovs'ka
author: Maxim Volodymyrovych Tkachuk
published in: Ukrainian Mathematical Journal
publication date: 2012-03-19T00:00:00Z
review text: \textit{G. Aumann} [Ann. Math. (2) 37, 443--447 (1936; Zbl 0014.03406)] showed that a compact set in \(\mathbb{R}^d\) is convex if all its intersections with planes of a fixed dimension are empty or homology cells. For later results see p. 26 of [\textit{P. Mani-Levitska}, Characterizations of convex sets, Handbook of convex geometry. Volume A. Amsterdam: North-Holland. 19--41 (1993; Zbl 0847.52001)] and [\textit{L. Montejano} and \textit{F. V. Shchepin}, Bull. Lond. Math. Soc. 28, No. 5, 501--504 (1996; Zbl 0863.52004)]. The present paper gives related results and extends them to quaternionic \(d\)-space.
reviewed by: Erhard Heil
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 6015949
zbMATH Keywords: criteria for convexity
zbMATH Keywords: acyclic support set
zbMATH Keywords: acyclic intersection
zbMATH Keywords: quaternionic space
MaRDI profile type: Publication
full work available at URL: s11253-011-0522-z
OpenAlex ID: W2081221400
cites work: On a topological characterization of compact convex point sets
cites work: Strong hypercomplex convexity
cites work: Criterion for convexity of a domain of a Euclidean space
DOI: 10.1007/S11253-011-0522-Z
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description: scientific article; zbMATH DE number 6015949