Displaying similar documents to “Classifying finite-sheeted covering mappings of paracompact spaces.”

Covering maps over solenoids which are not covering homomorphisms

Katsuya Eda, Vlasta Matijević (2013)

Fundamenta Mathematicae

Similarity:

Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and...

Generalized universal covering spaces and the shape group

Hanspeter Fischer, Andreas Zastrow (2007)

Fundamenta Mathematicae

Similarity:

If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception...