A semifilter approach to selection principles

2004/12/27 by Lubomyr Zdomsky, Zdomsky, Lubomyr · 2 citations
Computer Science · Mathematics · #03E17 #03E35 (Secondary) #54D20 (Primary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis #math.CO #math.GN #msc:03E17 #msc:03E35 #msc:54D20

paper · pdf · doi:10.48550/arxiv.math/0412498

LaTeX 2e, 15 pages, submitted to Comment. Math. Univ. Carolinae

arxiv created 2004/12/27 · openalex publication_date 2004/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the semifilter approach to the classical Menger and Hurewicz covering properties and show that the small cardinal g is a lower bound of the additivity number of the family of Menger subspaces of the Baire space, and under u< g every subset X of the real line with the property Split(Lambda,Lambda) is Hurewicz.

Cited by

• Universally meager sets in the Miller model and similar ones
• A density counterpart of the Scheepers covering property

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