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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Irreducible representations of normal spaces
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by Leonard R. Rubin PDF
Proc. Amer. Math. Soc. 107 (1989), 277-283 Request permission

Abstract:

We define the notion of irreducible polyhedral representation of a normal space making use of approximate inverse systems. This generalizes the concept of irreducible polyhedral expansions introduced in 1937 by Freudenthal for metric compacta and generalized to uniform spaces by Isbell in 1961. We show that every normal space $X$ has an irreducible polyhedral representation whose dimension is $X$ and whose weight is weight $(X)$. Approximate inverse systems were first introduced by S. Mardešić and this author. The concept generalizes that of inverse system and was essentially used in proving that each Hausdorff compactum of integral cohomological dimension $\leq n$ is the cell-like image of a Hausdorff compactum of covering dimension $\leq n$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 277-283
  • MSC: Primary 54F45; Secondary 54B25
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0991708-3
  • MathSciNet review: 991708