engleski

Classifying Finite-Sheeted Covering Mappings of Paracompact Spaces

The well-known classical classification theorem of the covering space theory refers to covering mappings of connected spaces, where the base space is is loccaly pathwise connected and semi-locally 1-connected. Here, we give a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. It establishes a bijection between the set of all pointed equivalence classes of s-sheeted pointed covering mappings f:(X, *)→ (Y, *) over connected paracompact space (Y, *) and the set of all subprogroups of index s of the fundamental progroup of (Y, *). In the unpointed case it establishes a bijection the set of all equivalence classes of s-sheeted covering mappings f:X→ Y and the set of all conjugacy classes of subprogroups of index s of the fundamental progroup of (Y, *), where * is arbitrary chosen point of Y.

Shape; resolution; inverse system; overlay; covering mapping; paracompact space; fundamental progroup.

nije evidentirano