NSS and TAP properties in topological groups close to being compact

2009/09/12 by Dikran Dikranjan, Dikranjan, Dikran, Dmitri Shakhmatov +3
Mathematics · #22A05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GN #math.GR #msc:22A05

paper · pdf · doi:10.48550/arxiv.0909.2381

arxiv created 2009/09/12 · openalex publication_date 2009/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of productivity (summability) of sequences in a topological group G, parametrized by a given function f : N --> omega+1. The extreme case when f is the function taking constant value omega is closely related to the TAP property, the weaker version of the well-known property NSS. We prove that TAP property coincides with NSS in locally compact groups, omega-bounded abelian groups and countably compact minimal abelian groups. As an application of our results, we provide a negative answer to [13, Question 11.1].

Citations

• Metrizable TAP, HTAP and STAP groups

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• Group-valued continuous functions with the topology of pointwise convergence

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