Christopher Caruvana
Published 2023-03-21Version 1
In this note, we characterize when the Vietoris space of compact subsets of a given space has the Hurewicz property in terms of a selection principle on the given space itself using $k$-covers and the notion of groupability introduced by Ko\v{c}inac and Scheepers. Using similar techniques, we also establish another equivalent condition to a space being Hurewicz in each of its finite powers.
The Vietoris hyperspace of finite sets of Erdős space
Selective screenability and the Hurewicz property
On $θ$-Hurewicz and $α$-Hurewicz Topological spaces
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