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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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An AR-map whose range is more infinite-dimensional than its domain
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by J. J. Dijkstra, J. van Mill and J. Mogilski PDF
Proc. Amer. Math. Soc. 114 (1992), 279-285 Request permission

Abstract:

We construct an example of an AR-map $f:X \to Y$, where $X$ is a strongly countable dimensional compact AR and $Y$ is a countable dimensional AR which is not strongly countable dimensional. Using this map we find a shrinkable decomposition of the pre-Hilbert space $l_f^2$ whose quotient map does not stabilize to a near homeomorphism. We also present a partial result concerning the question whether cell-like maps preserve countable dimensionality.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 279-285
  • MSC: Primary 54C55; Secondary 54G20, 57N20
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1075946-X
  • MathSciNet review: 1075946