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Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika, 2024, Number 87, Pages 5–10
DOI: https://doi.org/10.17223/19988621/87/1
(Mi vtgu1051)
 

MATHEMATICS

About the properties of spaces $C_p(X)$ close to Frechet–Urysohn property

O. O. Badmaev

Tomsk State University, Tomsk, Russian Federation
References:
Abstract: By analogy with the Fréchet-Urysohn property, the properties of $n$-Fréchet-Urysohn and $\omega$-Fréchet-Urysohn spaces of the spaces $C_p(X)$ are introduced into consideration. The connection between these properties and the properties $\gamma_n'$ and $\gamma_\omega'$ of the space $X$ is studied. In particular, it is established that the property $\gamma_\omega'$ of the space $X$ is equivalent the $\omega$-Frechet-Urysohn property of the space $C_p(X)$, and also that from the $n$-Frechet-Urysohn property it follows $\gamma_n'$.
Keywords: $\omega$-cover, $\gamma$-property, Gerlits-Nagy property, Frechet Urysohn property, $\gamma_k'$-property, Lindelof property, $\omega$-Fréchet-Urysohn, $n$-Fréchet-Urysohn.
Received: 21.07.2023
Accepted: February 12, 2024
Document Type: Article
UDC: 515.1
MSC: 54D20
Language: Russian
Citation: O. O. Badmaev, “About the properties of spaces $C_p(X)$ close to Frechet–Urysohn property”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2024, no. 87, 5–10
Citation in format AMSBIB
\Bibitem{Bad24}
\by O.~O.~Badmaev
\paper About the properties of spaces $C_p(X)$ close to Frechet--Urysohn property
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2024
\issue 87
\pages 5--10
\mathnet{http://mi.mathnet.ru/vtgu1051}
\crossref{https://doi.org/10.17223/19988621/87/1}
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    Вестник Томского государственного университета. Математика и механика
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