Locally unbounded topological fields with topological nilpotents

J. E. Marcos ¹

¹ Departamento Algebra y Geometría Facultad de Ciencias 47005 Valladolid, Spain

Fundamenta Mathematicae, Tome 173 (2002) no. 1, pp. 21-32

Résumé

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.

Détail

DOI : 10.4064/fm173-1-2

Keywords: construct locally unbounded topological fields having topologically nilpotent elements answers question heine underlying fields subfields fields formal power series particular get locally unbounded topological field which set topologically nilpotent elements additive subgroup exhibit complete locally unbounded topological field which topological extension field p adic numbers topological field missing example classification complete first countable fields given mutylin