## 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

classificaton

Zbl 0989.57002
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