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Acta Mathematica Hungarica

, Volume 128, Issue 4, pp 358–368 | Cite as

Covering properties which, under weak diamond principles, constrain the extents of separable spaces

  • C. Morgan
  • S. G. Da Silva
Article

Abstract

We show that separable, locally compact spaces with property (a) necessarily have countable extent — i.e., have no uncountable closed, discrete subspaces — if the effective weak diamond principle ⋄(ω,ω,<) holds. If the stronger, non-effective, diamond principle Φ(ω,ω,<) holds then separable, countably paracompact spaces also have countable extent. We also give a short proof that the latter principle implies there are no small dominating families in ω 1 ω.

Key words and phrases

locally compact space property (a) parametrized weak diamond principle countable paracompactness 

2000 Mathematics Subject Classification

primary 54D20, 54A25, 03E65 secondary 54D45, 54A35, 03E05, 03E35, 03E75 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Instituto de MatemáticaUniversidade Federal da BahiaSalvadorBrazil

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