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Результаты исследований: Вклад в журнал › Статья › Рецензирование
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TY - JOUR
T1 - On the product of almost discrete Grothendieck spaces
AU - Osipov, A. V.
PY - 2024
Y1 - 2024
N2 - A topological space X is called almost discrete, if it has precisely one nonisolated point. In this paper, we get that for a countable product X=∏Xi of almost discrete spaces Xi the space Cp(X) of all continuous real-valued functions with the topology of pointwise convergence is a μ-space if, and only if, X is a weak q-space if, and only if, t(X)=ω if, and only if, X is functionally generated by the family of all its countable subspaces. This result makes it possible to solve Archangel'skii's problem on the product of Grothendieck spaces. It is proved that in the model of ZFC, obtained by adding one Cohen real, there are Grothendieck spaces X and Y such that X×Y is not weakly Grothendieck space. In (PFA): the product of any countable family almost discrete Grothendieck spaces is a Grothendieck space. © 2024 Elsevier B.V.
AB - A topological space X is called almost discrete, if it has precisely one nonisolated point. In this paper, we get that for a countable product X=∏Xi of almost discrete spaces Xi the space Cp(X) of all continuous real-valued functions with the topology of pointwise convergence is a μ-space if, and only if, X is a weak q-space if, and only if, t(X)=ω if, and only if, X is functionally generated by the family of all its countable subspaces. This result makes it possible to solve Archangel'skii's problem on the product of Grothendieck spaces. It is proved that in the model of ZFC, obtained by adding one Cohen real, there are Grothendieck spaces X and Y such that X×Y is not weakly Grothendieck space. In (PFA): the product of any countable family almost discrete Grothendieck spaces is a Grothendieck space. © 2024 Elsevier B.V.
UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85191328098
U2 - 10.1016/j.topol.2024.108919
DO - 10.1016/j.topol.2024.108919
M3 - Article
VL - 350
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
M1 - 108919
ER -
ID: 56638942