Inner-distal homeomorphisms

Aponte J.; Donoso S.; Villavicencio H. · Topology and its Applications (2026) · DOI: 10.1016/j.topol.2026.109952

Resumen

We introduce inner-distal homeomorphisms of compact metric spaces, namely homeomorphisms whose proximal cells have empty interior. We show that inner-distality imposes nontrivial dynamical restrictions on perfect compact metric spaces: every transitive inner-distal homeomorphism has a set of periodic points with empty interior. We place inner-distality within the hierarchy of generalized distality notions, proving that countably distal homeomorphisms are inner-distal and that every cw –distal homeomorphism on a perfect locally connected compact metric space is inner-distal. We also establish preservation under semi-open extensions and invariance under topological conjugacy. Motivated by Baire category, we introduce the stronger notion of meagre-distality . We prove that meagre-distal homeomorphisms admit uncountably many almost periodic points and stable classes, cannot be densely Li–Yorke chaotic, and do not satisfy the two-sided limit shadowing property.

Instituciones: Universidad Nacional de Ingeniería