On small homotopies of loops

DOI10.1016/j.topol.2008.01.009zbMath1148.57030arXiv0712.1722OpenAlexW2009316174MaRDI QIDQ929992

Andreas Zastrow, Matjaž Željko, Gregory R. Conner, Mark H. Meilstrup, Dušan D. Repovš

Publication date: 19 June 2008

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.1722

zbMATH Keywords

Peano continuumPath space1-ULCHomotopically HausdorffShape injective

Mathematics Subject Classification ID

Algebraic topology of manifolds (57N65) Surgery obstructions, Wall groups (57R67) Poincaré duality spaces (57P10) Surgery obstructions ((K)-theoretic aspects) (19J25)

Related Items (17)

Fundamental groups of James reduced products ⋮ INFINITARY COMMUTATIVITY AND ABELIANIZATION IN FUNDAMENTAL GROUPS ⋮ On quasi-small loop groups ⋮ Homotopical smallness and closeness ⋮ On semilocally simply connected spaces ⋮ A natural pseudometric on homotopy groups of metric spaces ⋮ On small \(n\)-Hawaiian loops ⋮ Thick Spanier groups and the first shape group ⋮ Homotopy properties of subsets of Euclidean spaces ⋮ On the fundamental group of inverse limits ⋮ On fundamental groups with the quotient topology ⋮ Transfinite product reduction in fundamental groupoids ⋮ Dense products in fundamental groupoids ⋮ Scattered products in fundamental groupoids ⋮ Test map characterizations of local properties of fundamental groups ⋮ Small loop spaces ⋮ On the failure of the first Čech homotopy group to register geometrically relevant fundamental group elements

Cites Work

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• Generalized universal covering spaces and the shape group
• On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane
• On shape
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