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Property $ C$ and fine homotopy equivalences


Authors: Jan van Mill and Jerzy Mogilski
Journal: Proc. Amer. Math. Soc. 90 (1984), 118-120
MSC: Primary 54F45; Secondary 55P10
DOI: https://doi.org/10.1090/S0002-9939-1984-0722429-5
MathSciNet review: 722429
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Abstract: 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.


References [Enhancements On Off] (What's this?)

  • [An] R. D. Anderson, A continuous curve admitting monotone open maps onto all locally connected metric continua, Bull. Amer. Math. Soc. 62 (1956), 264.
  • [Bo] K. Borsuk, Theory of shape, PWN, Warsaw, 1975. MR 0418088 (54:6132)
  • [Cu] D. W. Curtis, Hyperspaces of finite subsets, preprint.
  • [Ha1] W. E. Haver, Mappings between ANR's that are fine homotopy equivalences, Pacific J. Math. 58 (1975), 457-461. MR 0385865 (52:6724)
  • [Ha2] -, A covering property for metric spaces, Topology Conference Virginia Polytechnic Institute and State University (R. F. Dickman and P. Fletcher, eds.), Lecture Notes in Math., vol. 375, Springer-Verlag, Berlin and New York, 1974, pp. 108-113. MR 0365504 (51:1756)
  • [ko] G. Kozlowski, Images of ANR's, preprint.
  • [To] H. Toruńnczyk, Concerning locally homotopy negligible sets and characterization of $ {l_2}$-manifolds, Fund. Math. 101 (1978), 93-110. MR 518344 (80g:57019)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0722429-5
Keywords: Fine homotopy equivalence, countable dimension, property $ C$, sigma compact linear spaces, Hilbert cube
Article copyright: © Copyright 1984 American Mathematical Society

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