2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63178The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste Italy 200119 pages, one figureGeometric TopologyAlgebraic Topology57N15; 55R65text