2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173882We construct an example of a real-valued continuous non-constant function $f$ defined on a connected complete metric space $X$ such that every point of $X$ is a point of local minimum or local maximum for $f$. The space $X$ is connected but fails to be separably connected.5 pagesGeneral TopologyMetric Geometry54D05; 54C30text