The Hurewicz Property and the Vietoris Hyperspace

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 Kočinac 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 Kočinac.

arXiv commentNoted that Theorems 49 and 50 answer a question of Kocinac

References in corpus (2)

• Selection Games and the Vietoris Space
• The Hurewicz covering property and slaloms in the Baire space