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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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Property $C$ and fine homotopy equivalences
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by Jan van Mill and Jerzy Mogilski PDF
Proc. Amer. Math. Soc. 90 (1984), 118-120 Request permission


We show that within the class of metric $\sigma$-compact spaces, proper fine homotopy equivalences preserve property $C$, which is a slight generalization of countable dimensionality. We also give an example of an open fine homotopy equivalence of a countable dimensional space onto a space containing the Hilbert cube.
    R. D. Anderson, A continuous curve admitting monotone open maps onto all locally connected metric continua, Bull. Amer. Math. Soc. 62 (1956), 264.
  • Karol Borsuk, Theory of shape, Monografie Matematyczne, Tom 59, PWN—Polish Scientific Publishers, Warsaw, 1975. MR 0418088
  • D. W. Curtis, Hyperspaces of finite subsets, preprint.
  • William E. Haver, Mappings between $\textrm {ANR}$s that are fine homotopy equivalences, Pacific J. Math. 58 (1975), no. 2, 457–461. MR 385865, DOI 10.2140/pjm.1975.58.457
  • William E. Haver, A covering property for metric spaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 108–113. MR 0365504
  • G. Kozlowski, Images of ANR’s, preprint.
  • H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $l_{2}$-manifolds, Fund. Math. 101 (1978), no. 2, 93–110. MR 518344, DOI 10.4064/fm-101-2-93-110
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 118-120
  • MSC: Primary 54F45; Secondary 55P10
  • DOI:
  • MathSciNet review: 722429