Strong shape and homology
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Bibliographic Information
Strong shape and homology
（Springer monographs in mathematics）
Springer, c2000
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Includes bibliographical references (p. [465]-477) and indexes
Description and Table of Contents
Description
Shape theory, an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces, was introduced by Borsuk 30 years ago and Mardesic contributed greatly to it. One expert says: "If we need a book in the field, this is it! It is thorough, careful and complete."
Table of Contents
I. Coherent Homotopy.- 1. Coherent mappings.- 2. Coherent homotopy.- 3. Coherent homotopy of sequences.- 4. Coherent homotopy and localization.- 5. Coherent homotopy as a Kleisli category.- II. Strong Shape.- 6. Resolutions.- 7. Strong expansions.- 8. Strong shape.- 9. Strong shape of metric compacta.- 10. Selected results on strong shape.- III. Higher Derived Limits.- 11. The derived functors of lim.- 12. limn and the extension functors Extn.- 13. The vanishing theorems.- 14. The cofinality theorem.- 15. Higher limits on the category pro-Mod.- IV. Homology Groups.- 16. Homology pro-groups.- 17. Strong homology groups of systems.- 18. Strong homology on CH(pro-Top).- 19. Strong homology of spaces.- 20. Spectral sequences. Abelian groups.- 21. Strong homology of compact spaces.- 22. Generalized strong homology.- References.- List of Special Symbols.- Author Index.
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