Simply connected spaces
Tudor Ganea (1951)
Fundamenta Mathematicae
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Tudor Ganea (1951)
Fundamenta Mathematicae
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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...
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...
A. Lelek, Jan Mycielski (1961)
Fundamenta Mathematicae
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Michael Barr, Radu Diaconescu (1981)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Eric Robinson (1979)
Fundamenta Mathematicae
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N. Brodskiy, J. Dydak, B. Labuz, A. Mitra (2012)
Fundamenta Mathematicae
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We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and...
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...
J. Hunt (1980)
Fundamenta Mathematicae
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Vlasta Matijevic (2003)
Revista Matemática Complutense
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The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and...
Charatonik, J.J. (1996)
Portugaliae Mathematica
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Rudolph Hrycay (1970)
Fundamenta Mathematicae
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