Contractibility of half-spaces of partial convexity
type: Item
instance of: scholarly article
title: Contractibility of half-spaces of partial convexity
zbMATH Open document ID: 1183.52005
DOI: 10.1134/S0001434609050277
author: V. G. Naidenko
published in: Mathematical Notes
publication date: 2009-11-10T00:00:00Z
review text: The author of this paper deals with the following Fink-Wood conjecture: every connected half-space of partial convexity (convexity with respect to a set of directions, or of directing hyperplanes) is contractible in \(\mathbb{R}^n\) if the set of directing hyperplanes has the point intersection property. A counterexample is constructed in the three-dimensional space, proving that there is a connected non-simply-connected half-space of orthoconvexity not verifying the Fink-Wood conjecture. However, it is shown that this conjecture stays valid in case of directed half-spaces of partial convexity. Thus, the main result presented in this paper is: every directed half-space \(X\) of partial convexity, in the linear \(n\)-dimensional space, is contractible provided that the set of directing hyperplanes has the point intersecting property.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 5628218
zbMATH Keywords: directed half-space
zbMATH Keywords: Fink-Wood problem
zbMATH Keywords: half-space of partial convexity
zbMATH Keywords: orthoconvexity
zbMATH Keywords: partial convexity
MaRDI profile type: Publication
cites work: Partial convexity
cites work: Algorithmic aspects of partial convexity
cites work: Restricted-orientation convexity.
cites work: Classification of semispaces according to their types in infinite-dimensional vector spaces
description: scientific article; zbMATH DE number 5628218