Abstract:We provide examples of spaces satisfying generalized combinatorial covering properties such as the Hurewicz, Menger, and $\gamma$-properties in an uncountable setting. Our approach is motivated by canonical constructions from the classical countable case, including the examples of Bartoszyński and Shelah separating the Hurewicz property from $\sigma$-compactness, the examples of Tsaban and Zdomskyy separating the Hurewicz and Menger properties, and Tsaban's construction of a nontrivial set of reals with the $\gamma$-property. We focus on the genuinely nontrivial aspects of these higher-cardinal generalizations, uncovering several open problems whose nature appears substantially different from that of their countable counterparts.
From: Piotr Szewczak [view email]
[v1]
Mon, 15 Jun 2026 16:37:00 UTC (43 KB)
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