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Noncompact hereditarily strongly infinite-dimensional spaces


Author: Leonard R. Rubin
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
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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 [Enhancements On Off] (What's this?)

  • [A] P. S. Aleksandrov, The present status of the theory of dimension, Amer. Math. Soc. Transl. (2) 1 (1955), 1–26. MR 0073983
  • [Bi] 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
  • [Ch] T. A. Chapman, Lectures on Hilbert cube manifolds, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR 0423357
  • [He] David W. Henderson, An infinite-dimensional compactum with no positive-dimensional compact subsets—a simpler construction, Amer. J. Math. 89 (1967), 105–121. MR 0210072, https://doi.org/10.2307/2373100
  • [H] W. Hurewicz, Une remarque sur l'hypothese du continu, Fund. Math. 19 (1932), 8-9.
  • [H-W] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • [K] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
  • [R] Leonard R. Rubin, Hereditarily strongly infinite-dimensional spaces, Michigan Math. J. 27 (1980), no. 1, 65–73. MR 555838
  • [R-S-W] 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
  • [W] John J. Walsh, Infinite-dimensional compacta containing no 𝑛-dimensional (𝑛≥1) subsets, Topology 18 (1979), no. 1, 91–95. MR 528239, https://doi.org/10.1016/0040-9383(79)90017-X
  • [Z] 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

DOI: https://doi.org/10.1090/S0002-9939-1980-0560602-6
Keywords: Strong infinite dimension, essential family, continuum-wise separator, Z-set
Article copyright: © Copyright 1980 American Mathematical Society