Locally unbounded topological fields with topological nilpotents

J. E. Marcos. "Locally unbounded topological fields with topological nilpotents." Fundamenta Mathematicae 173.1 (2002): 21-32. <http://eudml.org/doc/283133>.

@article{J2002,
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.},
author = {J. E. Marcos},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {21-32},
title = {Locally unbounded topological fields with topological nilpotents},
url = {http://eudml.org/doc/283133},
volume = {173},
year = {2002},
}

TY - JOUR
AU - J. E. Marcos
TI - Locally unbounded topological fields with topological nilpotents
JO - Fundamenta Mathematicae
PY - 2002
VL - 173
IS - 1
SP - 21
EP - 32
AB - 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.
LA - eng
UR - http://eudml.org/doc/283133
ER -