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

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.

### MSC:

 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.)

### Keywords:

filter; Hurewicz property; Menger property

Zbl 0870.03021
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