The product of a Lindelöf space with the space of irrationals under Martin’s axiom
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- by K. Alster PDF
- Proc. Amer. Math. Soc. 110 (1990), 543-547 Request permission
Abstract:
In this paper, we give an example of a Lindelöf space whose product with the space of irrationals is not Lindelöf provided that Martin’s axiom holds. Our result is an improvement of a Michael’s construction using the Continuum Hypothesis.References
- D. K. Burke and S. W. Davis, Subsets of $^{\omega }\omega$ and generalized metric spaces, Pacific J. Math. 110 (1984), no. 2, 273–281. MR 726486, DOI 10.2140/pjm.1984.110.273
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1983. An introduction to independence proofs; Reprint of the 1980 original. MR 756630
- Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 543-547
- MSC: Primary 54B10; Secondary 03E50, 54D20
- DOI: https://doi.org/10.1090/S0002-9939-1990-0993736-9
- MathSciNet review: 993736