Spaces which admit AR-resolutions
HTML articles powered by AMS MathViewer
- by A. Koyama, S. Mardešić and T. Watanabe PDF
- Proc. Amer. Math. Soc. 102 (1988), 749-752 Request permission
Abstract:
It is proved that a topological space $X$ admits an AR-resolution (in the sense of [6]) if and only if $X$ has trivial (strong) shape.References
- T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), no. 3, 181–193. MR 320997, DOI 10.4064/fm-76-3-181-193
- Ju. T. Lisica and S. Mardešić, Steenrod-Sitnikov homology for arbitrary spaces, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 2, 207–210. MR 707958, DOI 10.1090/S0273-0979-1983-15156-X
- Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and a strong shape category of topological spaces, Topology (Leningrad, 1982) Lecture Notes in Math., vol. 1060, Springer, Berlin, 1984, pp. 164–173. MR 770236, DOI 10.1007/BFb0099932
- Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and strong shape theory, Glas. Mat. Ser. III 19(39) (1984), no. 2, 335–399 (English, with Serbo-Croatian summary). MR 790021
- Sibe Mardešić, Decreasing sequences of cubes and compacta of trivial shape, General Topology and Appl. 2 (1972), 17–23. MR 301715
- Sibe Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), no. 1, 53–78. MR 643305, DOI 10.4064/fm-114-1-53-78
- Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 749-752
- MSC: Primary 54B25; Secondary 54C55, 54C56
- DOI: https://doi.org/10.1090/S0002-9939-1988-0929015-6
- MathSciNet review: 929015