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

Matijević, Vlasta

Rev. Mat. Complut. 16, No. 1, 311-327 (2003).

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.

Reviewer: Emil Molnár (Budapest)

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