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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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Volume 17, Issue 4

Issues

A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes

Marilyn Breen
Published Online: 2017-10-07 | DOI: https://doi.org/10.1515/advgeom-2017-0031

Abstract

Let 𝓒 be a finite family of distinct boxes in ℝd, let S = ⋃ {C : C in 𝓒} and let G be the intersection graph of 𝓒. For each block of G, assume that the corresponding members of 𝓒 have a staircase convex union. Then S with the rectilinear metric is a median space. Moreover, if every two points of S see a common point via staircase paths in S, then S is staircase starshaped.

Keywords: Orthogonal polygon; staircase convex set; staircase starshaped set; median space

MSC 2010: Primary 52.A30; 52.A35

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About the article


Received: 2015-09-13

Revised: 2016-02-07

Published Online: 2017-10-07

Published in Print: 2017-10-26


Citation Information: Advances in Geometry, Volume 17, Issue 4, Pages 525–532, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0031.

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Marilyn Breen
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2018

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