There is a $Q$-set space in ZFC
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- by Zoltán T. Balogh
- Proc. Amer. Math. Soc. 113 (1991), 557-561
- DOI: https://doi.org/10.1090/S0002-9939-1991-1077786-3
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Abstract:
It is shown that there is a regular ${T_1}$-space whose every subset is a ${G_\delta }$-set and yet the space is not $\sigma$-discrete.References
- Zoltán Balogh and Heikki Junnila, Totally analytic spaces under $V=L$, Proc. Amer. Math. Soc. 87 (1983), no. 3, 519–527. MR 684650, DOI 10.1090/S0002-9939-1983-0684650-3
- William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4
- William G. Fleissner, Roger W. Hansell, and Heikki J. K. Junnila, PMEA implies proposition $\textrm {P}$, Topology Appl. 13 (1982), no. 3, 255–262. MR 651508, DOI 10.1016/0166-8641(82)90034-7
- R. W. Hansell, Some consequences of $(V=L)$ in the theory of analytic sets, Proc. Amer. Math. Soc. 80 (1980), no. 2, 311–319. MR 577766, DOI 10.1090/S0002-9939-1980-0577766-0
- Heikki J. K. Junnila, Some topological consequences of the product measure extension axiom, Fund. Math. 115 (1983), no. 1, 1–8. MR 690665, DOI 10.4064/fm-115-1-1-8
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
- Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
- G. M. Reed, On normality and countable paracompactness, Fund. Math. 110 (1980), no. 2, 145–152. MR 600588, DOI 10.4064/fm-110-2-145-152
- Mary Ellen Rudin, Dowker’s set theory question, Questions Answers Gen. Topology 1 (1983), no. 2, 75–76. MR 722085 —, A topology on $c$ which yields a ${T_3}$ non-$\sigma$-discrete space in which every subset is a ${G_\delta }$ set, handwritten manuscript.
- Saharon Shelah, Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR 675955, DOI 10.1007/978-3-662-21543-2
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 557-561
- MSC: Primary 54G20; Secondary 54H05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1077786-3
- MathSciNet review: 1077786