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Completions of paratopological groups and bounded sets

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Abstract

In this paper we consider two questions in the realm of paratopological groups: When does multiplication on a given Tychonoff paratopological group H admit an extension to continuous multiplication on the Dieudonné completion, \(\mu {H}\), of H in such a way that H turns into a dense subgroup of the paratopological group \(\mu {H}\)? and, if A and B are bounded subsets of paratopological groups G and H, respectively, is \(A\times B\) bounded in \(G\times H\)? The motivation for these questions comes from the field of topological groups and they are receiving a special attention as an interesting source of open problems.

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Authors and Affiliations

  1. Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Castellón de la Plana, Spain

    Manuel Sanchis

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana (Iztapalapa campus), Mexico, DF, Mexico

    Mikhail Tkachenko

Authors
  1. Manuel Sanchis
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  2. Mikhail Tkachenko
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Correspondence to Manuel Sanchis.

Additional information

Communicated by A. Constantin.

The first author was supported by Universitat Jaume I Grant P1-1B2014-35 and Generalitat Valenciana Grant AICO/2016/030.

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Sanchis, M., Tkachenko, M. Completions of paratopological groups and bounded sets. Monatsh Math 183, 699–721 (2017). https://doi.org/10.1007/s00605-016-0953-6

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