Subbase countable compact- ness

Z. Szentmiklóssy; István Juhász; J. Gerlits

doi:10.1556/sscmath.38.2001.1-4.15

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 38: Issue 1-4

Subbase countable compact- ness

Authors:

Z. Szentmiklóssy

Z. Szentmiklóssy Eötvös Loránd Tudományegyetem Analízis Tanszék Pázmány Péter sétány 1/c H-1117 Budapest Hungary

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István Juhász

István Juhász Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics HU–1364 Budapest

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J. Gerlits

J. Gerlits Magyar Tudományos Akadémia Rényi Alfréd Matematikai Kutatóintézet Postafiók 127 H-1364 Budapest Hungary

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Pages:: 225–231

Online Publication Date:: 22 Jul 2005

Publication Date:: 01 May 2001

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.38.2001.1-4.15

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A topological space X is S -countably compact for a subbase S of X if for any infinite subset A ˆ X there is an S -accumulation point p 2 X of A, i.e. any member of S containing the point p contains infinitely many points of A. AspaceXis called subbase countably compact (in short: SCC) if there is a subbase S of X such that X is S -countably compact. We show that SCC is a productive property, any discrete space of size at least continuum is SCC, but SCC implies countable compactness for X if the Lindel¨ of-degree of X is SCC, but SCC implies countable compactness for X if the Lindel¨ of-degree of X

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Studia Scientiarum Mathematicarum Hungarica

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Studia Scientiarum Mathematicarum Hungarica
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