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On the product of almost discrete Grothendieck spaces. / Osipov, A. V.
In: Topology and its Applications, Vol. 350, 108919, 2024.

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Harvard

Osipov, AV 2024, 'On the product of almost discrete Grothendieck spaces', Topology and its Applications, vol. 350, 108919. https://doi.org/10.1016/j.topol.2024.108919

APA

Osipov, A. V. (2024). On the product of almost discrete Grothendieck spaces. Topology and its Applications, 350, [108919]. https://doi.org/10.1016/j.topol.2024.108919

Vancouver

Osipov AV. On the product of almost discrete Grothendieck spaces. Topology and its Applications. 2024;350:108919. doi: 10.1016/j.topol.2024.108919

Author

Osipov, A. V. / On the product of almost discrete Grothendieck spaces. In: Topology and its Applications. 2024 ; Vol. 350.

BibTeX

@article{6facf2d9582e484e9124d0460cb9f857,
title = "On the product of almost discrete Grothendieck spaces",
abstract = "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. {\textcopyright} 2024 Elsevier B.V.",
author = "Osipov, {A. V.}",
year = "2024",
doi = "10.1016/j.topol.2024.108919",
language = "English",
volume = "350",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",

}

RIS

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