The intermediate value theorem over a non-Archimedean field via Hensel's Lemma

2013/12/03 by L. Corgnier, Corgnier, L., Carla Massaza +3
Mathematics · #12J15 #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1312.0877

openalex publication_date 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's Lemma for restricted power series is the main tool of the proof.

Related

• On the Intermediate Value Theorem over a Valued Field
• Double series over a non-Archimedean field
• On functions given by algebraic power series over Henselian valued fields
• Series and power series on universally complete complex vector lattices
• The last proof of extreme value theorem and intermediate value theorem