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On sets every homeomorphic image of which has the Baire property


Author: John C. Morgan II
Journal: Proc. Amer. Math. Soc. 75 (1979), 351-354
DOI: https://doi.org/10.1090/S0002-9939-79-99959-3
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Abstract | References | Additional Information

Abstract: It is shown that the class of sets every homeomorphic image of which has the Baire property does not coincide with the class of sets which have the Baire property in the restricted sense.


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

  • [1] M. Lavrentieff, Contribution à la théorie des ensembles homéomorphes, Fund. Math. 6 (1924), 149-160.
  • [2] John C. Morgan II, On the absolute Baire property, Pacific J. Math. 78 (1978), no. 2, 415–431. MR 519763
  • [3] W. Sierpiński, Sur une propriété topologique des ensembles dénombrables denses en soi, Fund. Math. 1 (1920), 11-16.
  • [4] E. Szpilrajn (Marczewski), O zbiorach i funcjach bezwzglednie mierzalnych, C R. Soc. Sci. Varsovie 30 (1937), 39-68. (An English translation of this article is available.)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-79-99959-3
Keywords: Baire category, Baire property, scattered set, homeomorphism, analogies between category and measure
Article copyright: © Copyright 1979 American Mathematical Society

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