Equivalent characterizations of non-Archimedean uniform spaces

Daniel Windisch

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


In this paper, we deal with uniform spaces given by a system of non-Archimedean pseudo-metrics. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because uniformities stemming from valuations or directed systems of ideals are of this type.

In general, apart from systems of pseudo-metrics, there are two further approaches to the concept of uniform spaces: covering uniformities and diagonal uniformities. For each of these ways of defining a uniformity, we isolate a non-Archimedean special case and show that these special cases themselves correspond to systems of non-Archimedean pseudo-metrics.

Moreover, we formulate a separation axiom that tells exactly when a topology is induced by a non-Archimedean uniformity. In analogy to the classical metrizability theorems, we characterize when a non-Archimedean uniformity comes from a single pseudo-metric.
Original languageEnglish
Title of host publicationAlgebraic, Number Theoretic, and Topological Aspects of Ring Theory
Place of PublicationCham
ISBN (Electronic)978-3-031-28847-0
ISBN (Print)978-3-031-28846-3
Publication statusPublished - 2023
Event2021 Conference on Rings and Polynomials - Graz, Austria
Duration: 19 Jul 202124 Jul 2021


Conference2021 Conference on Rings and Polynomials


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