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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Collapsible polyhedra and median spaces
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by M. van de Vel PDF
Proc. Amer. Math. Soc. 126 (1998), 2811-2818 Request permission

Abstract:

It is shown that a collapsible, compact, connected, simplicial polyhedron admits a cubical subdivision and a median convexity, such that all cubes are convex subspaces with a convexity of subcubes. Conversely, a compact, connected, cubical polyhedron with a convexity as described admits a collapsible simplicial subdivision. Such a convexity, when it exists, is uniquely determined by the corresponding cubical presentation. Some related open problems have been formulated.
References
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Additional Information
  • M. van de Vel
  • Affiliation: Fakulteit Wiskunde en Informatika, Vrije Universiteit, NL-1081 HV Amsterdam, the Netherlands
  • Email: marcel@cs.vu.nl
  • Received by editor(s): February 22, 1996
  • Received by editor(s) in revised form: February 5, 1997

  • Dedicated: This paper is dedicated to the memory of my son Wouter, 1974–1993
  • Communicated by: Christopher Croke
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2811-2818
  • MSC (1991): Primary 57Q99, 52A01; Secondary 05C99
  • DOI: https://doi.org/10.1090/S0002-9939-98-04413-X
  • MathSciNet review: 1452832