A note on Michael’s problem concerning the Lindelöf property in the Cartesian products

Alster, K.

doi:10.1090/S0002-9947-1983-0697081-1

A note on Michael’s problem concerning the Lindelöf property in the Cartesian products
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by K. Alster

Trans. Amer. Math. Soc. 278 (1983), 369-375

DOI: https://doi.org/10.1090/S0002-9947-1983-0697081-1

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Abstract:

In this note we present a sketch of a negative solution of the Michael’s conjecture which says that if the product $Y \times X$ is Lindelöf for every hereditarily Lindelöf space $Y$, then $Y \times {X^\omega }$ is Lindelöf for every hereditarily Lindelöf space $Y$.

References

K. Alster, A class of spaces whose Cartesian product with every hereditarily Lindelöf space is Lindelöf, Fund. Math. 114 (1981), no. 3, 173–181. MR 644402, DOI 10.4064/fm-114-3-173-181
K. Alster, Some remarks on Michael’s question concerning Cartesian products of Lindelöf spaces, Colloq. Math. 47 (1982), no. 1, 23–29. MR 679380, DOI 10.4064/cm-47-1-23-29

On Michael’s problem concerning the Lindelöf property in the Cartesian products

Ryszard Engelking, Topologia ogólna, Biblioteka Matematyczna [Mathematics Library], vol. 47, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1975 (Polish). MR 0500779
Z. Frolík, On the topoligical product of paracompact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 747–750 (English, with Russian summary). MR 125559
N. Noble, Products with closed projections. II, Trans. Amer. Math. Soc. 160 (1971), 169–183. MR 283749, DOI 10.1090/S0002-9947-1971-0283749-X
Roman Pol, A function space $C(X)$ which is weakly Lindelöf but not weakly compactly generated, Studia Math. 64 (1979), no. 3, 279–285. MR 544732, DOI 10.4064/sm-64-3-279-285
Rastislav Telgársky, $C$-scattered and paracompact spaces, Fund. Math. 73 (1971/72), no. 1, 59–74. MR 295293, DOI 10.4064/fm-73-1-59-74