3 papers
math.CA2022
On a new measure on the Levi-Civita field
Mateo Restrepo Borrero, Vatsal Srivastava, Khodr Shamseddine
The Levi-Civita field is the smallest non-Archimidean ordered field extension of the real numbers that is real closed and Cauchy complete in the topology induced by t…
math.FA2021
On the analyticity of WLUD functions of one variable and WLUD functions of several variables in a complete non-Archimedean valued field
Khodr Shamseddine
Let be a non-Archimedean ordered field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order, and whose Hahn grou…
math.FA2019
On the topological structure of the Hahn field and convergence of power series
Darren Flynn, Khodr Shamseddine
In this paper, we study the topological structure of the Hahn field whose elements are functions from the additive abelian group of rational numbers to the real numbers field, with…