On an additive modification of the $\gamma$-property

O. O. Badmaev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 5-11

Résumé

For Tikhonov spaces, a sequence $(\gamma'_{k})_{k\omega}$ of topological properties is defined, each of which is not stronger than the classical Gerlich–Nagy property ($\gamma$-property), and $\gamma'_{k +1}$ follows from $\gamma'_{k}$. The behavior of the index k under standard topological operations is studied. As one of the main results, it was established that, in contrast to the $\gamma$-property, taking a topological sum does not take the sequence $(\gamma'_{k})_{k\omega}$ outside the sequence, but only leads to addition indices. In addition, the connection of the sequence $(\gamma'_{k})_{k\omega}$ with the Lindelof property was found, as well as some other facts.

Détail

Keywords: $\omega$-cover, $\gamma$-property, Gerlits–Nagy property, $\gamma'_{k}$ -property, Lindelöf property.