Ultrafilter selection and Corson compacta

0562139 - MÚ 2023 RIV ES eng J - Journal Article
Bonnet, R. - Kubiś, Wieslaw - Todorčević, S.
Ultrafilter selection and Corson compacta.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 116, č. 4 (2022), č. článku 178. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Boolean algebras * Corson compact spacs * elementary submodel * ultrafilter selection * Valdivia compact spaces
OECD category: Pure mathematics
Impact factor: 2.9, year: 2022
Method of publishing: Limited access
https://doi.org/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.
Permanent Link: https://hdl.handle.net/11104/0334552