2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73956The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify the fundamental group pi1(HA) as a quotient of the Hawaiian earring group, provide a precise description of the kernel, show that both pi1(HA) and the kernel are uncountable, and that pi1(HA) has the indiscrete topology.6 pagesAlgebraic TopologyGeneral Topology57S30text