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Classifying finite-sheeted covering mappings of paracompact spaces. (English) Zbl 1060.57003

Recently, S. Mardešić and 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.

MSC:

57M10 Covering spaces and low-dimensional topology
55P55 Shape theory
55Q07 Shape groups
54B35 Spectra in general topology
54C56 Shape theory in general topology

Keywords:

classificaton

Citations:

Zbl 0989.57002
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