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A totally ordered Baire space for which Blumberg's theorem fails


Author: Ronnie Levy
Journal: Proc. Amer. Math. Soc. 41 (1973), 304
MSC: Primary 54C30
DOI: https://doi.org/10.1090/S0002-9939-1973-0324630-4
Erratum: Proc. Amer. Math. Soc. 45 (1974), 469.
MathSciNet review: 0324630
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Abstract: An elementary example of a totally ordered nonBlumberg Baire space is given.


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

  • [1] H. Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), 113-128. MR 1501216
  • [2] J. C. Bradford and C. Goffman, Metric spaces in which Blumberg's theorem holds, Proc. Amer. Math. Soc. 11 (1960), 667-670. MR 26 #3832. MR 0146310 (26:3832)
  • [3] L. Gillman and M. Jerison, Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #6994. MR 0116199 (22:6994)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324630-4
Keywords: Baire space, Blumberg space, $ P$-space, $ {\eta _1}$-set
Article copyright: © Copyright 1973 American Mathematical Society

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