publication . Preprint . 2015

On topological groups admitting a base at identity indexed with $\omega^\omega$

Leiderman, Arkady G.; Pestov, Vladimir G.; Tomita, Artur H.;
Open Access English
  • Published: 22 Nov 2015
Abstract
A topological group $G$ is said to have a local $\omega^\omega$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\omega^\omega$. In particular, every metrizable group is such, but the class of groups with a local $\omega^\omega$-base is significantly wider. The aim of this article is to better understand the boundaries of this class, by presenting new examples and counter-examples. Ultraproducts and non-arichimedean ordered fields lead to natural families of non-metrizable groups with a local $\omega^\omega$-base which nevertheless are Baire topological spaces. More examples come from such constructions as the fre...
Subjects
arXiv: Mathematics::General Topology
free text keywords: Mathematics - General Topology, 22A05
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