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A weakly infinite-dimensional space whose product with the irrationals is strongly infinite-dimensional


Author: Elżbieta Pol
Journal: Proc. Amer. Math. Soc. 98 (1986), 349-352
MSC: Primary 54F45; Secondary 54B10
DOI: https://doi.org/10.1090/S0002-9939-1986-0854045-0
MathSciNet review: 854045
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an example of a weakly infinite-dimensional space $ X$ such that the product $ X \times B$ of $ X$ and a subspace $ B$ of the irrationals is strongly infinite-dimensional; under the assumption of the Continuum Hypothesis, $ B$ can be the irrationals. This example answers a question of Addis and Gresham [AG].


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  • [AG] D. F. Addis and J. H. Gresham, A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandroff 's problem, Fund. Math. 101 (1978), 195-205. MR 521122 (80b:54041)
  • [AP] P. S. Alexandroff and B. A. Pasynkov, Introduction to dimension theory, Nauka, Moskva, 1973. (Russian)
  • [E] R. Engelking, Dimension theory, PWN, Warszawa, 1978. MR 0482697 (58:2753b)
  • [EP] R. Engelking and E. Pol, Countable-dimensional spaces: A survey, Dissertationes Math. 216 (1983), 1-41. MR 722011 (85f:54075)
  • [H] W. E. Haver, A covering property for metric spaces, Lecture Notes in Math., vol. 375, Springer-Verlag, Berlin and New York, 1974, pp. 108-113. MR 0365504 (51:1756)
  • [K] K. Kuratowski, Topology, vols. I, II, PWN, Warszawa, 1966, 1968. MR 0217751 (36:840)
  • [M] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376. MR 0152985 (27:2956)
  • [P1] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), 634-636. MR 614892 (82f:54059)
  • [P2] -, A remark on $ A$-weakly infinite-dimensionalspaces, Topology Appl. 13 (1982), 97-101. MR 637431 (83b:54051)
  • [RSW] L. R. Rubin, R. M. Shori, and J. J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), 93-103. MR 519716 (80e:54049)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0854045-0
Keywords: Weakly infinite-dimensional spaces, products, property $ C$
Article copyright: © Copyright 1986 American Mathematical Society

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