Locally unbounded topological fields with topological nilpotents

Volume 173 / 2002

J. E. Marcos Fundamenta Mathematicae 173 (2002), 21-32 MSC: Primary 12J99. DOI: 10.4064/fm173-1-2

Abstract

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 field is a missing example in the classification of complete first countable fields given by Mutylin.

Authors

  • J. E. MarcosDepartamento Algebra y Geometría
    Facultad de Ciencias
    47005 Valladolid, Spain
    e-mail

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