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Mat. Zametki, 2009, Volume 85, Issue 6, Pages 915–926 (Mi mz3913)  

This article is cited in 2 scientific papers (total in 2 papers)

Contractibility of Half-Spaces of Partial Convexity

V. G. Naidenko

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: The Fink–Wood problem on the contractibility of half-spaces of partial convexity is studied. It is proved that there exists a connected non-simply-connected half-space of orthoconvexity in the three-dimensional space, which disproves the Fink–Wood conjecture in the general case. In a special case, it is proved that, if the set of directions of partial convexity contains a basis of the linear $n$-dimensional space, then all directed half-spaces of partial convexity are contractible.

Keywords: partial convexity, orthoconvexity, half-space of partial convexity, directed half-space, Fink–Wood problem

DOI: https://doi.org/10.4213/mzm3913

Full text: PDF file (449 kB)
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English version:
Mathematical Notes, 2009, 85:6, 868–876

Bibliographic databases:

UDC: 514+681.3
Received: 21.06.2007
Revised: 11.02.2008

Citation: V. G. Naidenko, “Contractibility of Half-Spaces of Partial Convexity”, Mat. Zametki, 85:6 (2009), 915–926; Math. Notes, 85:6 (2009), 868–876

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Dulliev, “Properties of Connected Ortho-convex Sets in the Plane”, Math. Notes, 101:3 (2017), 443–459  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. M. Dulliev, “Two Structures Based on Convexities on the 2-Sphere”, Math. Notes, 102:2 (2017), 156–163  mathnet  crossref  crossref  mathscinet  isi  elib
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