2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168540We prove that a `small' extension of a minimal AF equivalence relation on a Cantor set is orbit equivalent to the AF relation. By a `small' extension we mean an equivalence relation generated by the minimal AF equivalence relation and another AF equivalence relation which is defined on a closed thin subset. The result we obtain is a generalization of the main theorem in [GMPS2].12 pagesDynamical SystemsOperator Algebras37B05text