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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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Universal spaces for almost $n$-dimensionality
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by Mohammad Abry and Jan J. Dijkstra PDF
Proc. Amer. Math. Soc. 135 (2007), 2623-2628 Request permission

Abstract:

We find universal functions for the class of lower semi-continuous (LSC) functions with at most $n$-dimensional domain. In an earlier paper we proved that a space is almost $n$-dimensional if and only if it is homeomorphic to the graph of an LSC function with an at most $n$-dimensional domain. We conclude that the class of almost $n$-dimensional spaces contains universal elements (that are topologically complete). These universal spaces can be thought of as higher-dimensional analogues of complete Erdős space.
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Additional Information
  • Mohammad Abry
  • Affiliation: Faculteit der Exacte Wetenschappen / Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081${}^a$, 1081 HV Amsterdam, The Netherlands
  • Email: mabry@cs.vu.nl
  • Jan J. Dijkstra
  • Affiliation: Faculteit der Exacte Wetenschappen / Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081${}^a$, 1081 HV Amsterdam, The Netherlands
  • MR Author ID: 58030
  • Email: dijkstra@cs.vu.nl
  • Received by editor(s): November 12, 2005
  • Published electronically: March 22, 2007
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2623-2628
  • MSC (2000): Primary 54F45, 54C25
  • DOI: https://doi.org/10.1090/S0002-9939-07-08971-X
  • MathSciNet review: 2302584