Some observations on filters with properties defined by open covers. (English) Zbl 1349.54054

Hernández-Gutiérrez, Rodrigo; Szeptycki, Paul J.

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)

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