Stability theorems in shape and pro-homotopy
HTML articles powered by AMS MathViewer
- by David A. Edwards and Ross Geoghegan
- Trans. Amer. Math. Soc. 222 (1976), 389-403
- DOI: https://doi.org/10.1090/S0002-9947-1976-0423347-2
- PDF | Request permission
Abstract:
Conditions are given under which a topological space has the pointed shape of a CW complex. These are derived from analogous conditions in pro-homotopy.References
- M. Artin and B. Mazur, Etale homotopy, Lecture Notes in Mathematics, No. 100, Springer-Verlag, Berlin-New York, 1969. MR 0245577, DOI 10.1007/BFb0080957
- Karol Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223–254. MR 229237, DOI 10.4064/fm-62-3-223-254
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573, DOI 10.1007/978-3-540-38117-4
- C. H. Dowker, Homology groups of relations, Ann. of Math. (2) 56 (1952), 84–95. MR 48030, DOI 10.2307/1969768
- David A. Edwards and Ross Geoghegan, The stability problem in shape, and a Whitehead theorem in pro-homotopy, Trans. Amer. Math. Soc. 214 (1975), 261–277. MR 413095, DOI 10.1090/S0002-9947-1975-0413095-6
- David A. Edwards and Ross Geoghegan, Shapes of complexes, ends of manifolds, homotopy limits and the Wall obstruction, Ann. of Math. (2) 101 (1975), 521–535. MR 375330, DOI 10.2307/1970939
- David A. Edwards and Harold M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, Vol. 542, Springer-Verlag, Berlin-New York, 1976. MR 0428322, DOI 10.1007/BFb0081083
- Ralph H. Fox, On shape, Fund. Math. 74 (1972), no. 1, 47–71. MR 296914, DOI 10.4064/fm-74-1-47-71
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- D. M. Hyman, A remark on Fox’s paper on shape, Fund. Math. 75 (1972), no. 3, 205–208. MR 303498, DOI 10.4064/fm-75-3-205-208
- G. Kozlowski and J. Segal, Locally well-behaved paracompacta in shape theory, Fund. Math. 95 (1977), no. 1, 55–71. MR 442926, DOI 10.4064/fm-95-1-55-71 J. Levan, Doctoral dissertation, Univ. of Kentucky, 1973.
- Sibe Mardešić, Shapes for topological spaces, General Topology and Appl. 3 (1973), 265–282. MR 324638, DOI 10.1016/0016-660X(72)90018-9
- James Keesling, On the Whitehead theorem in shape theory, Fund. Math. 92 (1976), no. 3, 247–253. MR 431156, DOI 10.4064/fm-92-3-247-253
- Sibe Mardešić and Jack Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (1971), no. 1, 41–59. MR 298634, DOI 10.4064/fm-72-1-41-59
- Sibe Mardešić and Jack Segal, Equivalence of the Borsuk and the ANR-system approach to shapes, Fund. Math. 72 (1971), no. 1, 61–68. (errata insert). MR 301694, DOI 10.4064/fm-72-1-61-68
- J. Peter May, Simplicial objects in algebraic topology, Van Nostrand Mathematical Studies, No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0222892
- Kiiti Morita, On shapes of topological spaces, Fund. Math. 86 (1975), no. 3, 251–259. MR 388385, DOI 10.4064/fm-86-3-251-259 T. Porter, Čech homotopy. I, II, J. London Math. Soc. (2) 6 (1973), 429-436, 667-675. MR 47 #9613; 50 #8517a.
- Timothy Porter, Stability results for topological spaces, Math. Z. 140 (1974), 1–21. MR 385846, DOI 10.1007/BF01218642
- Jean-Louis Verdier, Équivalence essentielle des systèmes projectifs, C. R. Acad. Sci. Paris 261 (1965), 4950–4953 (French). MR 190209
- C. T. C. Wall, Finiteness conditions for $\textrm {CW}$-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 171284, DOI 10.2307/1970382
- Kiiti Morita, The Hurewicz and the Whitehead theorems in shape theory, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 12 (1974), 246–258. MR 372848
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 222 (1976), 389-403
- MSC: Primary 55D99
- DOI: https://doi.org/10.1090/S0002-9947-1976-0423347-2
- MathSciNet review: 0423347