### A generalization of Čech-complete spaces and Lindelöf $\Sigma $-spaces

The class of $s$-spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf $p$-spaces, metrizable spaces with the weight $\le {2}^{\omega}$, but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that $s$-spaces are in a duality with Lindelöf $\Sigma $-spaces: $X$ is an $s$-space if and only if some (every) remainder of $X$ in a compactification is a Lindelöf $\Sigma $-space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. 220 (2013),...