The algebraic closure of a $p$-adic number field is a complete topological field

Rok, strany: 2006, 317 - 331

The algebraic closure of a $p$-adic field is not a complete field with the $p$-adic topology. We define another field topology on this algebraic closure so that it is a complete field. This new topology is finer than the $p$-adic topology and is not provided by any absolute value. Our topological field is a complete, not locally bounded and not first countable field extension of the $p$-adic number field, which answers a question of Mutylin.

ISO 690:

Marcos, J. 2006. The algebraic closure of a $p$-adic number field is a complete topological field. In Mathematica Slovaca, vol. 56, no.3, pp. 317-331. 0139-9918.

APA:

Marcos, J. (2006). The algebraic closure of a $p$-adic number field is a complete topological field. Mathematica Slovaca, 56(3), 317-331. 0139-9918.