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

O. O. Badmaev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 5-10

Résumé

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 $\gamma_n'$.

Détail

Keywords: $\omega$-cover, $\gamma$-property, Gerlits-Nagy property, Frechet Urysohn property, $\gamma_k'$-property, Lindelof property, $\omega$-Fréchet-Urysohn, $n$-Fréchet-Urysohn.