A ZFC example (of minimum weight) of a Lindelöf space and a completely metrizable space with a nonnormal product

Lawrence, L.

doi:10.1090/S0002-9939-96-02864-X

A ZFC example (of minimum weight) of a Lindelöf space and a completely metrizable space with a nonnormal product
HTML articles powered by AMS MathViewer

by L. Brian Lawrence PDF

Proc. Amer. Math. Soc. 124 (1996), 627-632 Request permission

Abstract:

We give an example as indicated in the title where the weight (i.e., the minimum cardinality of a base for the topology) of the product is the smallest uncountable cardinal.

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
K. Alster and G. Gruenhage, Remarks on the product of Lindelöf spaces (to appear).
Amer Bešlagić, Normality in products, The work of Mary Ellen Rudin (Madison, WI, 1991) Ann. New York Acad. Sci., vol. 705, New York Acad. Sci., New York, 1993, pp. 17–46. MR 1277879, DOI 10.1111/j.1749-6632.1993.tb12523.x
L. Brian Lawrence, The influence of a small cardinal on the product of a Lindelöf space and the irrationals, Proc. Amer. Math. Soc. 110 (1990), no. 2, 535–542. MR 1021211, DOI 10.1090/S0002-9939-1990-1021211-4
E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3
Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502
Teodor C. Przymusiński, Products of normal spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 781–826. MR 776637