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- catalog abstract ""Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by polyhedra (ANRs) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes."--Jacket.".
- catalog contributor b11608414.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description ""Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by polyhedra (ANRs) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes."--Jacket.".
- catalog description "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. lim[superscript n] and the extension functors Ext[superscript n]. 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.".
- catalog description "Includes bibliographical references (p. [465]-477) and indexes.".
- catalog extent "xii, 489 p. :".
- catalog identifier "3540661980 (alk. paper)".
- catalog isPartOf "Springer monographs in mathematics".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog subject "514/.24 21".
- catalog subject "Homology theory.".
- catalog subject "QA612.7 .M353 2000".
- catalog subject "Shape theory (Topology)".
- catalog tableOfContents "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. lim[superscript n] and the extension functors Ext[superscript n]. 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.".
- catalog title "Strong shape and homology / Sibe Mardešić.".
- catalog type "text".