On the topological structure of the Levi-Civita field

DOI10.1016/j.jmaa.2010.02.018zbMath1190.26036OpenAlexW2042327908MaRDI QIDQ972483

Khodr Shamseddine

Publication date: 19 May 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.02.018

zbMATH Keywords

weak topologymetriccompact setabsorbing setclosed setlinear topological spaceorder topologynon-Archimedean fieldopen setcircled setvector topology

Mathematics Subject Classification ID

Non-Archimedean valued fields (12J25) Non-Archimedean analysis (26E30)

Related Items (7)

On Non-Archimedean Valued Fields: A Survey of Algebraic, Topological and Metric Structures, Analysis and Applications ⋮ Analysis on the Levi-Civita field and computational applications ⋮ Non-Archimedean transportation problems and Kantorovich ultra-norms ⋮ The implicit function theorem in a non-Archimedean setting ⋮ One-variable and multi-variable calculus on a non-Archimedean field extension of the real numbers ⋮ On the topological structure of a Hahn field and convergence of power series ⋮ On the solutions of linear ordinary differential equations and Bessel-type special functions on the Levi-Civita field

Cites Work

• Analytical properties of power series on Levi-Civita fields
• Generalized power series on a non-Archimedean 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
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