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arXiv · 2601.21734

Formalization of non-Archimedean functional analysis 1: spherically complete spaces

Yijun Yuan
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Abstract

In this article, we present a formalization of spherically complete spaces, a fundamental notion in non-Archimedean functional analysis, using the Lean theorem prover (v4.31.0), building over Mathlib. This work includes the equivalent definitions of spherically complete spaces, their basic properties, examples and non-examples such as the field $\mathbf{C}_p$ of $p$-adic complex numbers. As applications, we formalize the notion of Birkhoff-James orthogonality, the Hahn-Banach extension theorem and the spherical completion for non-Archimedean Banach spaces. URL of code: https://github.com/YijunYuan/SphericalCompleteness/tree/paper

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Yijun Yuan. 2026-01-29. Formalization of non-Archimedean functional analysis 1: spherically complete spaces. https://arxiv.org/abs/2601.21734

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