Formalization of non-Archimedean functional analysis 1: spherically complete spaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910022865256448 |
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| author | Yuan, Yijun |
| author_facet | Yuan, Yijun |
| contents | In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis. 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 Birkhoff-James orthogonality, Hahn-Banach extension theorem and the spherical completion for non-archimedean Banach spaces.
Code available at https://github.com/YijunYuan/SphericalCompleteness |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Formalization of non-Archimedean functional analysis 1: spherically complete spaces Yuan, Yijun Number Theory Logic in Computer Science Functional Analysis 46S10, 68V20, 12J25, 11S99 In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis. 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 Birkhoff-James orthogonality, Hahn-Banach extension theorem and the spherical completion for non-archimedean Banach spaces. Code available at https://github.com/YijunYuan/SphericalCompleteness |
| title | Formalization of non-Archimedean functional analysis 1: spherically complete spaces |
| topic | Number Theory Logic in Computer Science Functional Analysis 46S10, 68V20, 12J25, 11S99 |
| url | https://arxiv.org/abs/2601.21734 |