Authors: Bonnet, Robert
Kubiś, Wiesław
Todorčević, Stevo 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Ultrafilter selection and Corson compacta
Journal: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume: 116
First page: 178
Issue Date: 2022
Rank: ~M21a
ISSN: 1578-7303
DOI: 10.1007/s13398-022-01317-2
We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For cardinality ℵ1 the property is equivalent to the fact that the space of ultrafilters is not Corson compact. We also consider the pointwise topology on a Boolean algebra, proving a result on the Lindelöf number in the context of the ultrafilter selection property. Finally, we discuss poset Boolean algebras, interval algebras, and semilattices in the context of ultrafilter selection properties.
Keywords: Boolean algebras | Corson compact spacs | Elementary submodel | Ultrafilter selection | Valdivia compact spaces
Publisher: Springer Link

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