Some remarks on metric spaces whose product with every Lindelöf space is Lindelöf

Alster, K.

doi:10.1090/S0002-9939-99-04780-2

Some remarks on metric spaces whose product with every Lindelöf space is Lindelöf
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Proc. Amer. Math. Soc. 127 (1999), 2469-2473 Request permission

Abstract:

Let us assume that Martin’s Axiom holds. We prove that if $X$ is a metrizable space whose product with every Lindelöf space is Lindelöf, then for every metric $d$ on $X,$ consistent with the topology of $X, (X,d)$ is a countable union of totally bounded subsets.

References

K. Alster, The product of a Lindelöf space with the space of irrationals under Martin’s axiom, Proc. Amer. Math. Soc. 110 (1990), no. 2, 543–547. MR 993736, DOI 10.1090/S0002-9939-1990-0993736-9
K. Alster, Some remarks concerning the Lindelöf property of the product of a Lindelöf space with the irrationals, Proceedings of the Symposium on General Topology and Applications (Oxford, 1989), 1992, pp. 19–25. MR 1173239, DOI 10.1016/0166-8641(92)90075-B
Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
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