Productively Scheepers spaces and their relatives

2026/02/17 by Marta Kładź-Duda, Piotr Szewczak, Lyubomyr Zdomskyy · 1 voice
Mathematics · #math.GN

paper · pdf

Abstract

We prove that assuming \mathfrakb=\mathfrakd, in the class of hereditarily Lindelöf spaces, each productively Scheepers space is productively Hurewicz. The above statement remains true in the class of all general topological spaces assuming that \mathfrakd=ℵ₁. To this end we use combinatorial methods and the Menger covering property parametrized by ultrafilters. We also show that if near coherence of filters holds, then the Scheepers property is equivalent to a Menger property parametrized by any ultrafilter.

Citations

• Selection Principles in the Laver, Miller, and Sacks models
• Products of Luzin-type sets with combinatorial properties
• Finite powers and products of Menger sets
• Products of general Menger spaces
• Selective covering properties of product spaces
• Scales, fields, and a problem of Hurewicz
• A semifilter approach to selection principles
• Continuous images of sets of reals
• On the cofinality of ultrapowers
• The combinatorics of open covers (II)

Discussions

• Marta K{\l}ad\'z-Duda, Piotr Szewczak, Lyubomyr Zdomskyy: Productively Scheepers spaces and their relatives https://arxiv.org/abs/2602.16046 https://arxiv.org/pdf/2602.16046 https://arxiv.org/html/260 [bsky, 1 points, 0 comments]

Related

• Products of general Menger spaces
• Weak covering properties and selection principles
• On the interplay between productively Menger and productively Hurewicz spaces in models of \mathfrak b=\mathfrak d
• On certain weaker forms of the Scheepers property
• Selective covering properties of product spaces