Displaying similar documents to “Topological degrees of set-valued compact fields in locally convex spaces”

Fixed points of set-valued maps with closed proximally ∞-connected values

Grzegorz Gabor (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Introduction Many authors have developed the topological degree theory and the fixed point theory for set-valued maps using homological techniques (see for example [19, 28, 27, 16]). Lately, an elementary technique of single-valued approximation (on the graph) (see [11, 1, 13, 5, 9, 2, 6, 7]) has been used in constructing the fixed point index for set-valued maps with compact values (see [21, 20, 4]). In [20, 4] authors consider set-valued...

Locally unbounded topological fields with topological nilpotents

J. E. Marcos (2002)

Fundamenta Mathematicae

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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...

Properties of extensions of algebraically maximal fields.

G. Leloup (2003)

Collectanea Mathematica

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We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.