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arXiv · 2303.11768

The Hurewicz Property and the Vietoris Hyperspace

Christopher Caruvana
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Abstract

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. We comment that the same technique establishes another equivalent condition to a space being Hurewicz in each of its finite powers. We end with some characterizations involving spaces of continuous functions and answer a question posed by Ko\v{c}inac.

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Christopher Caruvana. 2023-03-21. The Hurewicz Property and the Vietoris Hyperspace. https://doi.org/10.1016/j.topol.2023.108670

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