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A solution to the Blumberg problem. (English) Zbl 0316.54011


MSC:

54C30 Real-valued functions in general topology
54G20 Counterexamples in general topology
03E05 Other combinatorial set theory
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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References:

[1] Henry Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), no. 2, 113 – 128. · JFM 49.0176.04
[2] J. C. Bradford and Casper Goffman, Metric spaces in which Blumberg’s theorem holds, Proc. Amer. Math. Soc. 11 (1960), 667 – 670. · Zbl 0178.56603
[3] P. R. Halmos, Lectures in Boolean algebras, Van Nostrand Reinhold, Toronto, 1972. · Zbl 0114.01603
[4] Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1 – 14. · Zbl 0245.02054 · doi:10.2307/2271510
[5] Ronnie Levy, A totally ordered Baire space for which Blumberg’s theorem fails, Proc. Amer. Math. Soc. 41 (1973), 304. · Zbl 0244.54009
[6] Ronnie Levy, Strongly non-Blumberg spaces, General Topology and Appl. 4 (1974), 173 – 177. · Zbl 0283.54006
[7] Edwin W. Miller, A note on Souslin’s problem, Amer. J. Math. 65 (1943), 673 – 678. · Zbl 0060.12701 · doi:10.2307/2371874
[8] H. E. White, Baire spaces for which Blumberg’s theorem does not hold(preprint). · Zbl 0307.54012
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