Cardinality restrictions on power homogeneous T5 compacta

Guit-Jan Ridderbos

doi:10.1556/sscmath.2008.1079

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 46: Issue 1

Cardinality restrictions on power homogeneous T₅ compacta

Author:

Guit-Jan Ridderbos

Guit-Jan Ridderbos Vrije Universiteit Faculty of Sciences, Division of Mathematics De Boelelaan 1081a 1081 HV Amsterdam the Netherlands

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Pages:: 113–120

Online Publication Date:: 17 Oct 2008

Publication Date:: 01 Mar 2009

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.2008.1079

Keywords:: Primary 03E35; 54A25; 54B10; 54D15; 54D30; Power homogeneity; compactum; tightness; cellularity

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We show that the cardinality of power homogeneous T₅ compacta X is bounded by 2 ^{c
(
X
)} . This answers a question of J. van Mill, who proved this bound for homogeneous T₅ compacta. We further extend some results of I. Juhász, P. Nyikos and Z. Szentmiklóssy and as a corollary we prove that consistently every power homogeneous T₅ compactum is first countable. This improves a theorem of R. de la Vega who proved this consistency result for homogeneous T₅ compacta.

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Studia Scientiarum Mathematicarum Hungarica

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Studia Scientiarum Mathematicarum Hungarica
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