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Covering maps for locally path-connected spaces

N. Brodskiy, J. Dydak, B. Labuz, A. Mitra (2012)

Fundamenta Mathematicae

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....

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