2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65530A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+α}$ diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy.14 pages, 4 figuresDynamical SystemsGeometric Topologytext