Wallman compactification and zero-dimensionality.

Arenas, F.G.; Sánchez-Granero, M.A.

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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 $\leq 2^{ω}$ , 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 $Σ$ -spaces: $X$ is an $s$ -space if and only if some (every) remainder of $X$ in a compactification is a Lindelöf $Σ$ -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math....

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