Arkhangel'skii's definition of cardinal function

Question

I was searching an article written by A. V. Arkhangel'skii called A theorem on Cardinality. I found it but there is a little problem: the article is in Russian. I can't read Russian and I need the definitions in the article. Particularly, the definition of the cardinal function $\text{qL}$. Here is the definition

I really aprecciate any help you can provide me.

Answer 1

I could guess from my minimal Russian but this paper confirms it, it's the quasi-Lindelöf number of $X$: the minimal infinite cardinality $\tau$ such that for all closed subsets $C$ of $X$ and all open covers $\mathcal{U}$ of $C$ (so that $C \subseteq \bigcup \mathcal{U}$) there is a subfamily $\mathcal{U}' \subseteq \mathcal{U}$ such that $|\mathcal{U}'| \le \tau$ and $C \subseteq \overline{\bigcup \mathcal{U}'}$.

(note that Arhangel'skij uses $[]$ for closure looking at the formula in the paper).