Michael spaces and Dowker planks

Agata Caserta, Stephen Watson

Abstract

We investigate the Lindelöf property of Dowker planks. In particular, we give necessary conditions such that the product of a Dowker plank with the irrationals is not Lindelöf. We also show that if there exists a Michael space, then, under some conditions involving singular cardinals, there is one that is a Dowker plank.

Keywords

Michael space; Michael function; NL property; Haydon plank

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References

M. Burke and M. Magidor, Shelah’s pcf theory and its applications, Ann. Pure Appl. Logic 50, (1990) 207–254. http://dx.doi.org/10.1016/0168-0072(90)90057-9

E. K. van Douwen, The integers and topology, in K. Kunen and J. Vaughan, editors, Handbook of Set-Theoretic Topology, 111–169, North-Holland, Amsterdam, (1984).

C. H. Dowker, Local dimension of normal spaces, Quart. J. Math. Oxford 2 (1990), no. 6, 101–120.

R. Engelking, General Topology, Heldermann Verlag, Berlin 1989.

R. Haydon, On compactness in spaces of measure and measure compact spaces, Proc. London Math. Soc. 29 (1974), no. 6, 1–16.

K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, Ams- terdam 1980.

E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. http://dx.doi.org/10.1090/S0002-9904-1963-10931-3

J. Tatch Moore, Some of the combinatorics related to Michael’s problem, Proc. Amer. Math. Soc. 127, (1999), no. 8, 2459–2467.

S. Watson, The Construction of Topological Spaces: Planks and Resolutions, in M. Husek and J. van Mill (eds.), Recent Progress in General Topology, 673–757, North-Holland 1992.

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Universitat Politècnica de València

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