Michael spaces and Dowker planks

Agata Caserta

Italy

Seconda Università degli Studi di Napoli

Dipartimento di Matematica

Stephen Watson

Canada

York University

Department of Mathematics and Statistics

Submitted: 2013-09-30

|

Accepted: 2013-09-30

|
DOI: https://doi.org/10.4995/agt.2009.1738
Funding Data

Downloads

Keywords:

Michael space, Michael function, NL property, Haydon plank

Supporting agencies:

This research was not funded

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.
Show more Show less

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.

Show more Show less