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lean-LCS: locally convex spaces, duality, and closed graph theorems in Lean 4

Bastiaan J. Braams

Palomar Registrypalomar/PALOMAR-2026-09-25-000007Sep 25, 2026math.FAscore 0

A Lean 4 formalization, built on Mathlib, of the basic theory of locally convex topological vector spaces over the real or complex numbers. It covers barrelled, quasi-barrelled, bornological and ultrabornological spaces; the closed graph and open mapping theorems for barrelled spaces, and Pták's closed graph and open mapping theorems; duality theory with the bipolar, Alaoglu–Bourbaki, Mackey, Mackey–Arens, Banach–Dieudonné and Krein–Šmulian theorems and Grothendieck's completeness theorem; semi-reflexive, reflexive and Montel spaces with their permanence properties; completeness of strong…

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