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

TL;DR

This paper demonstrates that power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on closed intervals, utilizing Hensel's Lemma for restricted power series.

Contribution

It extends the intermediate value theorem to non-Archimedean fields using Hensel's Lemma, a novel application in this mathematical context.

Findings

Power series over such fields satisfy the intermediate value theorem.

Hensel's Lemma is effective for proving properties of power series in non-Archimedean settings.

The result broadens understanding of analysis over non-Archimedean fields.

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.