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The regionally proximal relation for commutative semigroup actions

Angelina Blahodatna, Lauren Detmold, Daniel Glasscock, Anh N. Le

Palomar Registrypalomar/PALOMAR-2026-10-20-000017Oct 20, 2026math.DSscore 0

The regionally proximal relation and the equicontinuous structure relation are fundamental relations in topological dynamics that capture equicontinuous behaviour in a topological dynamical system and its factors. For minimal actions of abelian groups they are known to be equivalence relations and to coincide. This development formalizes in Lean 4 the results of the paper "The regionally proximal relation for commutative semigroup actions", which generalizes these facts from group actions to semigroup actions. Throughout, a system is an action of a discrete semigroup S on a compact Hausdorff…

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