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Titlebook: Geometric Topology and Shape Theory; Proceedings of a Con Sibe Mardešić,Jack Segal Conference proceedings 1987 Springer-Verlag Berlin Heide

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John M. Edington,M. Ann Edingtonoduce the class of nearly extendable multi-valued maps and prove that every acyclic upper semi-continuous nearly extendable multi-valued map of arbitrary compactum having Čech homology of finite type into itself with non-trivial Lefschetz numer has a fixed point.
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Sheaves that are locally constant with applications to homology manifolds, the orientation sheaf is locally constant. Additional applications appearing elsewhere include determining the homological local connectivity of decomposition spaces and providing dimension estimates of the images of closed mappings.
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0075-8434 versus cohomological dimension, ANR‘s and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.978-3-540-18443-0978-3-540-47975-8Series ISSN 0075-8434 Series E-ISSN 1617-9692
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Sheaves that are locally constant with applications to homology manifolds,lyses applies regardiess of the source of the presheaves, the applications involve either the homology presheaf and sheaf of a space or the cohomology presheaf and sheaf of a continuous function. Amongst the applications is an elementary proof that homology manifolds are locally orientable; that is,
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The intimate connections among decomposition theory, embedding theory, and manifold structure theor
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