Displaying similar documents to “Covering maps for locally path-connected spaces”

Generalized universal covering spaces and the shape group

Hanspeter Fischer, Andreas Zastrow (2007)

Fundamenta Mathematicae

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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...

Covering maps over solenoids which are not covering homomorphisms

Katsuya Eda, Vlasta Matijević (2013)

Fundamenta Mathematicae

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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...

Local homeomorphisms

Gerald F. Jungck

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CONTENTS1. Introduction and preliminaries..........................................52. Initial results.....................................................................73. H-Connected spaces......................................................114. Induced decompositions.................................................185. "Regular" decompositions...............................................256. An application and a generalization................................297. Locally separating...

On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane

G. R. Conner, J. W. Lamoreaux (2005)

Fundamenta Mathematicae

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We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result...

Ultra regular covering space and its automorphism group

Sang-Eon Han (2010)

International Journal of Applied Mathematics and Computer Science

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In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital...