Geodesic
About the properties of spaces $C_p(X)$ close to Frechet–Urysohn property
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 5-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : $\omega$-Fréchet-Urysohn, $n$-Fréchet-Urysohn. 
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     title = {About the properties of spaces $C_p(X)$ close to {Frechet{\textendash}Urysohn} property},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--10},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2024_87_a0/}
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O. O. Badmaev. About the properties of spaces $C_p(X)$ close to Frechet–Urysohn property. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 5-10. http://geodesic.mathdoc.fr/item/VTGU_2024_87_a0/

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[2] Arkhangelskii A.V., Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989, 222 pp.

[3] Osipov A.V., “Projective versions of the properties in the Scheepers Diagram”, Topology and its Applications, 278 (2020), 107232 | DOI | MR | Zbl