Michael spaces and Dowker planks

Authors

  • Agata Caserta Seconda Università degli Studi di Napoli
  • Stephen Watson York University

DOI:

https://doi.org/10.4995/agt.2009.1738

Keywords:

Michael space, Michael function, NL property, Haydon plank

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.

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Author Biographies

Agata Caserta, Seconda Università degli Studi di Napoli

Dipartimento di Matematica

Stephen Watson, York University

Department of Mathematics and Statistics

References

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

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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

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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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How to Cite

[1]
A. Caserta and S. Watson, “Michael spaces and Dowker planks”, Appl. Gen. Topol., vol. 10, no. 2, pp. 245–267, Oct. 2009.

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