Hernández-Gutiérrez, Rodrigo; Szeptycki, Paul J. Some observations on filters with properties defined by open covers. (English) Zbl 1349.54054 Commentat. Math. Univ. Carol. 56, No. 3, 355-364 (2015). In this paper the authors study covering properties of filters defined via the selection principles introduced in the paper by W. Just [Topology Appl. 73, No. 3, 241–266 (1996; Zbl 0870.03021)]. In particular, the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of \(P(\omega)\) with the Cantor set topology, are studied extensively with a lot of quite interesting results. In addition, several open questions are posed. Reviewer: Maximilian Ganster (Graz) Cited in 6 Documents MSC: 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.) Keywords:filter; Hurewicz property; Menger property Citations:Zbl 0870.03021 PDF BibTeX XML Cite \textit{R. Hernández-Gutiérrez} and \textit{P. J. Szeptycki}, Commentat. Math. Univ. Carol. 56, No. 3, 355--364 (2015; Zbl 1349.54054) Full Text: DOI arXiv OpenURL