NSS and TAP properties in topological groups close to being compact

Details NSS and TAP properties in topological groups close to being compact NSS and TAP properties in topological groups close to being compact

2009-09-12

arxiv.org/abs/0909.2381v1

Mathematics

General Topology

Scientific paper

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].

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