Inverse limits of covering spaces
Volume 269 / 2025
Fundamenta Mathematicae 269 (2025), 99-129
MSC: Primary 55Q05; Secondary 54A20, 57M10
DOI: 10.4064/fm231031-9-2
Published online: 24 April 2025
Abstract
Let $X$ be a Peano continuum (i.e., a metric space that is compact, connected and locally connected). We show that every path-connected inverse limit of covering spaces over $X$ is determined by its fundamental group and is homeomorphic to a quotient of the set of homotopy classes of based paths endowed with the shape topology.
