On Non-Archimedean Valued Fields: A Survey of Algebraic, Topological and Metric Structures, Analysis and Applications

DOI10.1007/978-3-030-81976-7_6zbMath1504.30065OpenAlexW4205468873MaRDI QIDQ5044589

Angel Barria Comicheo, Khodr Shamseddine

Publication date: 2 November 2022

Published in: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-81976-7_6

zbMATH Keywords

computational applicationsLevi-Civita fieldsnon-Archimedean analysisultrametric spacesnon-Archimedean valued fieldsnon-Archimedean calculusHahn fields

Mathematics Subject Classification ID

Non-Archimedean function theory (30G06)

Uses Software

• Cosy
• Tulliotools

Cites Work

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• On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers
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• Model theory.
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• The new theory of ultrametric spaces
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• On computational applications of the Levi-Civita field
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• Intermediate value theorem for analytic functions on a Levi-Civita field
• A local mean value theorem for functions on non-Archimedean field extensions of the real numbers
• Modell einer Leibnizschen Differentialrechnung mit aktual unendlich kleinen Grössen sämtlicher Ordnungen
• Measure theory and Lebesgue-like integration in two and three dimensions over the Levi-Civita field
• Summary on non-Archimedean valued fields
• Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem
• Characterization of compact and self-adjoint operators on free Banach spaces of countable type over the complex Levi-Civita field
• Valued Fields
• Ordered Vector Spaces
• Note on Hahn's Theorem on Ordered Abelian Groups
• Taylor's theorem, the inverse function theorem and the implicit function theorem for weakly locally uniformly differentiable functions on non-Archimedean spaces

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