Covering maps for locally path-connected spaces
N.Brodskiy, J.Dydak, B.Labuz, A.Mitra

TL;DR
This paper introduces Peano covering maps for locally path-connected spaces, characterizes their properties, and relates them to classical and generalized covering maps, providing new topological insights and conditions for their existence.
Contribution
It defines Peano covering maps, establishes their properties, and connects them with generalized regular coverings and subgroup topologies, expanding the classical theory.
Findings
Peano covering maps are locally path-connected in domain
They are characterized by homotopy lifting properties
A new topology on the universal cover characterizes path lifting
Abstract
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and Zastrow. If is path-connected, then every Peano covering map is equivalent to the projection , where is a subgroup of the fundamental group of and equipped with the basic topology. The projection is a Peano covering map if and only if it has the unique path lifting property. We define a new topology on for which one has a characterization…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory
