5 papers
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…
A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures
Hanna Ćmiel, Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordere…
Construction of ball spaces and the notion of continuity
René Bartsch, Katarzyna Kuhlmann, Franz-Viktor Kuhlmann
Spherically complete ball spaces provide a framework for the proof of generic fixed point theorems. For the purpose of their application it is important to have methods for the con…
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…