Strong shape theory and resolutions

DOI10.1016/0166-8641(83)90031-7zbMath0505.55012OpenAlexW2091323728MaRDI QIDQ1836425

Jack Segal, F. W. Cathey

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0166-8641(83)90031-7

zbMATH Keywords

fibrationcofibrationstrong shape theoryANR-resolutioncoherent lifting of the Cech shape functionSteenrod homotopy theory for pro-spaces

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Shape theory in general topology (54C56) Shape theory (55P55)

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Cites Work

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• Homotopical approach to strong shape or completion theory
• Realizing strong shape equivalences
• Cech and Steenrod homotopy theories with applications to geometric topology
• Homotopy limits and colimits
• Homotopical algebra
• The homotopy category is a homotopy category
• On fine shape theory
• Approximate polyhedra, resolutions of maps and shape fibrations
• Note on Cofibrations II.
• An exact sequence from the nth to the (n-1)-st fundamental group
• Shapes for topological spaces