Ultrafilter selection and Corson compacta

0562139 - MÚ 2023 RIV ES eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GF20-22230L
Institucionální podpora: RVO:67985840
Klíčová slova: Boolean algebras * Corson compact spacs * elementary submodel * ultrafilter selection * Valdivia compact spaces
Obor OECD: Pure mathematics
Impakt faktor: 2.9, rok: 2022
Způsob publikování: Omezený přístup
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.
Trvalý link: https://hdl.handle.net/11104/0334552