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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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A reduction of the fundamental conjecture about locally compact $\textrm {ANR}$’s
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by A. Fathi and Y. M. Visetti PDF
Proc. Amer. Math. Soc. 49 (1975), 446-448 Request permission

Abstract:

In this note, we show that the conjecture: the product of a locally compact ANR by the Hilbert cube is a Hilbert cube manifold, can be reduced to its compact AR case, i.e.: the product of a compact AR by the Hilbert cube is a Hilbert cube manifold.
References
    R. D. Anderson, T. A. Chapman and R. M. Schori, Problems in the topology of infinite dimensional spaces and manifolds, Mathematische Centrum, Amsterdam, 1971.
  • Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
  • T. A. Chapman, Notes on Hilbert cube manifolds, University of Kentucky, 1973 (preprint).
  • David W. Henderson, A simplicial complex whose product with any ANR is a simplicial complex, General Topology and Appl. 3 (1973), 81–83. MR 315659, DOI 10.1016/0016-660X(73)90033-0
  • Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
  • L. C. Siebenmann, L’invariance topologique du type simple d’homotopie, d’après T. A. Chapman, Sèminaire Bourbaki, Exposé 428, 1973.
  • H. Toruńczyk, Compact absolute retracts as factors of the Hilbert space, Fund. Math. 83 (1973), no. 1, 75–84. MR 326650, DOI 10.4064/fm-83-1-75-84
  • —, Absolute retracts as factors of normed linear spaces (preprint).
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 49 (1975), 446-448
  • MSC: Primary 57A20; Secondary 54F40
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0372866-0
  • MathSciNet review: 0372866