A Selection Principle and Products in Topological Groups

2022/05/26 by Marion Scheepers, Scheepers, Marion
Mathematics · #54H11 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Primary: 22A05 #Secondary: 54D20

paper · pdf · doi:10.48550/arxiv.2205.13132

openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the preservation under products, finite powers, and forcing, of a selection principle based covering property of T₀ topological groups. Though the paper is in part a survey, it contributes some new information, including: 1. The product of a strictly o-bounded group with an o-bounded group is an o-bounded group - Corollary 18 2. In the generic extension by a finite support iteration of ℵ₁ Hechler reals the product of any o-bounded group with a ground model ℵ₀ bounded group is an o-bounded group - Theorem 19 3. In the generic extension by a countable support iteration of length ℵ₂ Mathias reals the product of any o-bounded group with a ground model ℵ₀ bounded group is an o-bounded group - Theorem 20.

Related

• o-Boundedness of free objects over a Tychonoff space
• Selective screenability in topological groups
• Certain results on selection principles associated with bornological structure in topological spaces
• Selection Principles in the Laver, Miller, and Sacks models
• Products and selection principles