A semifilter approach to selection principles

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.

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

References in corpus (2)

• Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures
• The combinatorics of splittability

Cited by in corpus (13)

• Products of Menger spaces: a combinatorial approach
• On the Menger covering property and $D$-spaces
• Selective covering properties of product spaces
• Products of Menger spaces in the Miller model
• Combinatorial images of sets of reals and semifilter trichotomy
• o-Boundedness of free topological groups
• Products of Hurewicz spaces in the Laver model
• Selection Principles and special sets of reals: Open problems
• Menger's covering property and groupwise density
• Productively Lindelöf spaces and the covering property of Hurewicz
• M-separable spaces of functions are productive in the Miller model
• Coideals as remainders of groups distinguishing between combinatorial covering properties
• On the interplay between productively Menger and productively Hurewicz spaces in models of $\mathfrak{b}=\mathfrak{d}$