The implicit function theorem in a non-Archimedean setting

DOI10.1016/S0019-3577(09)80028-1zbMath1217.26063MaRDI QIDQ633042

Khodr Shamseddine, Trevor Rempel, Todd Sierens

Publication date: 31 March 2011

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

implicit function theoremreal closed fieldinverse function theoremnon-Archimedean field

Mathematics Subject Classification ID

Implicit function theorems, Jacobians, transformations with several variables (26B10) Non-Archimedean valued fields (12J25) Non-Archimedean analysis (26E30)

Related Items

Analysis on the Levi-Civita field and computational applications, A local mean value theorem for functions on non-Archimedean field extensions of the real numbers, A weaker smoothness criterion for the inverse function theorem, the intermediate value theorem, and the mean value theorem in a non-Archimedean setting, On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers, Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem

Cites Work

• On the solutions of linear ordinary differential equations and Bessel-type special functions on the Levi-Civita field
• Analytical properties of power series on Levi-Civita fields
• Generalized power series on a non-Archimedean field
• On the topological structure of the Levi-Civita field
• Fields: Algebraically closed and others
• Constrained second order optimization on non-archimedean fields
• Intermediate values and inverse functions on non-Archimedean fields
• Intermediate value theorem for analytic functions on a Levi-Civita field
• Algebraically Closed Fields Analogous to Fields of Puiseux Series
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