Displaying similar documents to “Topological groups of divisibility”

Locally solid topological lattice-ordered groups

Liang Hong (2015)

Archivum Mathematicum

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Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered...

Alexandroff One Point Compactification

Czesław Byliński (2007)

Formalized Mathematics

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In the article, I introduce the notions of the compactification of topological spaces and the Alexandroff one point compactification. Some properties of the locally compact spaces and one point compactification are proved.

Identifying and distinguishing various varieties of abelian topological groups

Carolyn E. McPhail, Sidney A. Morris

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A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally...

Locally unbounded topological fields with topological nilpotents

J. E. Marcos (2002)

Fundamenta Mathematicae

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We construct some locally unbounded topological fields having topologically nilpotent elements; this answers a question of Heine. The underlying fields are subfields of fields of formal power series. In particular, we get a locally unbounded topological field for which the set of topologically nilpotent elements is an open additive subgroup. We also exhibit a complete locally unbounded topological field which is a topological extension of the field of p-adic numbers; this topological...