Some observations on a clopen version of the Rothberger property
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Some observations on a clopen version of the Rothberger property
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| Автор |
Bhardwaj, M.
Osipov, A. V. |
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| Тематика |
POINT-CLOPEN GAME
SELECTION PRINCIPLES STRONG MEASURE ZERO ZERO-DIMENSIONAL SPACE |
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| Описание |
In this paper, we prove that a clopen version S1(CO, CO) of the Rothberger property and Borel strong measure ze-roness are independent. For a zero-dimensional metric space (X, d), X satisfies S1(CO, CO) if, and only if, X has Borel strong measure zero with respect to each metric which has the same topology as d has. In a zero-dimensional space, the game G1(O, O) is equivalent to the game G1(CO, CO) and the point-open game is equivalent to the point-clopen game. Us-ing reflections, we obtain that the game G1(CO, CO) and the point-clopen game are strategically and Markov dual. An example is given for a space on which the game G1(CO, CO) is undetermined. © 2023 Manoj Bhardwaj et al.
Ministry of Education and Science of the Russian Federation, Minobrnauka: 075-02-2023-913 The authors would like to thank the referees for careful reading and valuable comments. The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2023-913). |
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| Дата |
2024-04-05T16:36:38Z
2024-04-05T16:36:38Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Bhardwaj, M & Osipov, AV 2023, 'Some observations on a clopen version of the Rothberger property', Cubo, Том. 25, № 2, стр. 161-172. https://doi.org/10.56754/0719-0646.2502.161
Bhardwaj, M., & Osipov, A. V. (2023). Some observations on a clopen version of the Rothberger property. Cubo, 25(2), 161-172. https://doi.org/10.56754/0719-0646.2502.161 0716-7776 Final All Open Access, Gold, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85176922721&doi=10.56754%2f0719-0646.2502.161&partnerID=40&md5=e5b4a14c577c79d0c9bf8bee78eb84bd https://cubo.ufro.cl/ojs/index.php/cubo/article/download/3417/2296 http://elar.urfu.ru/handle/10995/130977 10.56754/0719-0646.2502.161 85176922721 001068779900001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by-nc https://creativecommons.org/licenses/by-nc/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Universidad de la Frontera
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| Источник |
Cubo (Temuco)
Cubo |
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