2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110043We characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopically 1-dimensional, we prove that each has fundamental group that embeds in the fundamental group of a 1-dimensional planar Peano continuum. We leave open the following question: Is a planar Peano continuum homotopically 1- dimensional if its fundamental group is isomorphic with the fundamental group of a 1-dimensional planar Peano continuum?18 pages, 2 figuresGeometric TopologyAlgebraic Topology54F50;55M10text