4 papers · 1 filter
Orderings and valuations in hyperfields
Katarzyna Kuhlmann, Alessandro Linzi, Hanna Stojałowska
We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induc…
Density of Composite Places in Function Fields and Applications to Real Holomorphy Rings
Eberhard Becker, Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
Given an algebraic function field and a place on , we prove that the places that are composite with extensions of to finite extensions of lie dense in the…
Embedding theorems for spaces of -places of rational function fields and their products
Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
We study spaces of -places of rational function fields in one variable. For extensions of formally real fields, with real closed and satisfying a nat…
A common generalization of metric, ultrametric and topological fixed point theorems - alternative version
Katarzyna Kuhlmann, Franz-Viktor Kuhlmann
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixe…