Classifying finite-sheeted covering mappings of paracompact spaces (Q1431102)

Recently, \textit{S. Mardešić} and \textit{V. Matijević} [Topology Appl. 113, No. 1--3, 167--209 (2001; Zbl 0989.57002)] classified indecomposable overlay structures over arbitrary connected topological spaces. Their classifiation theorem establishes a bijection between all pointed equivalence classes of \(s\)-sheeted indecomposable overlay structures over connected topological spaces \((Y,*)\) and all subgroups of index \(s\) of the fundamental progroup \(\pi_1(Y,*)\), \(*\) an arbitrary point of \(Y\). The main result of the present paper is a classification theorem (Th. 4 and 5) for finite-sheeted covering mappings over connected paracompact spaces. This is a generalization of the classical covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case.