A Stable Converse to the Vietoris-Smale Theorem with Applications to Shape Theory

DOI10.2307/1998371zbMath0452.57002OpenAlexW4246302959MaRDI QIDQ3899194

Steven C. Ferry

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/1998371

zbMATH Keywords

homotopy fiberapproximate fibrationshape equivalentapproximate homotopy lifting property(k+1)-connected map between compact Q-manifoldsLC(n)-continuumstable converse of the Vietoris-Smale TheoremUV(1)-compactumUV(k)-map

Mathematics Subject Classification ID

General topology of complexes (57Q05) Generalizations of fiber spaces and bundles in algebraic topology (55R65) Topology of infinite-dimensional manifolds (57N20) Shape theory in general topology (54C56) Shape theory (55P55) Homotopy and topological questions for infinite-dimensional manifolds (58B05) Shapes (aspects of topological manifolds) (57N25)

Related Items

Topological finiteness theorems for manifolds in Gromov-Hausdorff space, An inverse system approach to Menger manifolds, Continua that are shape-equivalent but not \(UV^ 1\)-equivalent, Shape Equivalence Does Not Imply Ce Equivalence, Realizing strong shape equivalences, An Example in Shape Theory, A Vietoris-Begle theorem for connective Steenrod homology theories and cell-like maps between metric compacta, Strong shape of compact Hausdorff spaces, Strong Shape for Topological Spaces, Empty components in strong shape theory, Desingularizing homology manifolds, Finiteness results in \(n\)-homotopy theory, CE equivalence and shape equivalence of LC\(^ n\) compacta, Cell-like images and UV\(^ m\) groups, Embeddings of Locally Connected Compacta, \(UV^ k\) maps and embeddings, Images of cell-like spaces, Shape theory, Unnamed Item, Minimal dynamics on Menger manifolds, Manifolds with non-stable fundamental groups at infinity, Local n-connectivity of decomposition spaces

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