A normal countably compact not absolutely countably compact space

Pavlov, Oleg

doi:10.1090/S0002-9939-01-05784-7

A normal countably compact not absolutely countably compact space
HTML articles powered by AMS MathViewer

by Oleg Pavlov PDF

Proc. Amer. Math. Soc. 129 (2001), 2771-2775 Request permission

Abstract:

We construct an example of a normal countably compact not absolutely countably compact space. We also prove that every hereditarily normal countably compact space is absolutely countably compact and suggest a method for construction of hereditarily normal spaces without property $(a)$.

References

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
W. M. Fleischman, A new extension of countable compactness, Fund. Math. 67 (1970), 1–9. MR 264608, DOI 10.4064/fm-67-1-1-9
Winfried Just, Michael V. Matveev, and Paul J. Szeptycki, Some results on property $(a)$, preprint.
Michael V. Matveev, Absolutely countably compact spaces, Topology Appl. 58 (1994), no. 1, 81–92. MR 1280711, DOI 10.1016/0166-8641(94)90074-4
M. V. Matveev, Some questions on property (a), Questions Answers Gen. Topology 15 (1997), no. 2, 103–111. MR 1472172
W. Pack, Absolutely countably compact topological groups, preprint.
Mary Ellen Rudin, Ian S. Stares, and Jerry E. Vaughan, From countable compactness to absolute countable compactness, Proc. Amer. Math. Soc. 125 (1997), no. 3, 927–934. MR 1415367, DOI 10.1090/S0002-9939-97-04030-6
Jerry E. Vaughan, On the product of a compact space with an absolutely countably compact space, Papers on general topology and applications (Amsterdam, 1994) Ann. New York Acad. Sci., vol. 788, New York Acad. Sci., New York, 1996, pp. 203–208. MR 1460834, DOI 10.1111/j.1749-6632.1996.tb36814.x