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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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Noncompact hereditarily strongly infinite-dimensional spaces
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by Leonard R. Rubin PDF
Proc. Amer. Math. Soc. 79 (1980), 153-154 Request permission

Abstract:

It is shown that any strongly infinite dimensional space contains a strongly infinite dimensional subspace all of whose subspaces are either 0-dimensional or strongly infinite dimensional.
References
  • P. S. Aleksandrov, The present status of the theory of dimension, Amer. Math. Soc. Transl. (2) 1 (1955), 1–26. MR 0073983, DOI 10.1090/trans2/001/01
  • R. H. Bing, A hereditarily infinite dimensional space, General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966) Academia, Prague, 1967, pp. 56–62. MR 0233336
  • T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357, DOI 10.1090/cbms/028
  • David W. Henderson, An infinite-dimensional compactum with no positive-dimensional compact subsets—a simpler construction, Amer. J. Math. 89 (1967), 105–121. MR 210072, DOI 10.2307/2373100
    • W. Hurewicz, Une remarque sur l’hypothese du continu, Fund. Math. 19 (1932), 8-9.
  • Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
  • Leonard R. Rubin, Hereditarily strongly infinite-dimensional spaces, Michigan Math. J. 27 (1980), no. 1, 65–73. MR 555838
  • Leonard R. Rubin, R. M. Schori, and John J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), no. 1, 93–102. MR 519716, DOI 10.1016/0016-660x(79)90031-x
  • John J. Walsh, Infinite-dimensional compacta containing no $n$-dimensional $(n\geq 1)$ subsets, Topology 18 (1979), no. 1, 91–95. MR 528239, DOI 10.1016/0040-9383(79)90017-X
    • A. V. Zarelua, Construction of strongly infinite-dimensional compacta using rings of continuous functions, Soviet Math. Dokl. 15 (1974), 106-110.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 79 (1980), 153-154
  • MSC: Primary 54F45
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0560602-6
  • MathSciNet review: 560602