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A note on infinite-dimension under refinable maps


Author: Hisao Kato
Journal: Proc. Amer. Math. Soc. 88 (1983), 177-180
MSC: Primary 54F45; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1983-0691304-6
MathSciNet review: 691304
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Abstract: It is shown that refinable maps preserve weak infinite-dimension, but not strong infinite-dimension.


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

  • [1] R. Engelking, Dimension theory, PWN, Warsaw, 1978. MR 0482697 (58:2753b)
  • [2] J. Ford and J. W. Rogers, Refinable maps, Colloq. Math. 39 (1978), 263-269. MR 522365 (80d:54009)
  • [3] W. Hurewicz and H. Wallman, Dimension theory, Van Nostrand, Princeton, N. J., 1948.
  • [4] H. Kato, Refinable maps in the theory of shape, Fund. Math. 113 (1981), 119-129. MR 640617 (83a:54048)
  • [5] I. Lončar and S. Mardešic, A note on inverse sequences of ANRs, Glasnik Math. 23 (1968), 41-48.
  • [6] P. R. Patten, Images of absolute neighborhood retracts and generalized absolute neighborhood retracts under refinable maps, Dissertation, University of Oklahoma, 1978.
  • [7] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), 634-636. MR 614892 (82f:54059)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691304-6
Keywords: Refinable maps, weak infinite-dimension, strong infinite-dimension, countable-dimension
Article copyright: © Copyright 1983 American Mathematical Society

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