A new proof of Funayama's theorem

Guram Bezhanishvili; Wesley H. Holliday

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arXiv · 2603.23464

A new proof of Funayama's theorem

Guram Bezhanishvili·Wesley H. Holliday

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Abstract

Funayama proved that a lattice embeds into a complete Boolean algebra in such a way that all existing joins and meets are preserved if and only if the lattice satisfies the join-infinite and meet-infinite distributive laws. There are several proofs of this classic result in the literature. In this note, we provide a new and purely order-theoretic proof of Funayama's theorem, as well as of generalizations of the theorem.

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Guram Bezhanishvili, Wesley H. Holliday. 2026-03-24. A new proof of Funayama's theorem. https://arxiv.org/abs/2603.23464

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