A Vietoris mapping theorem for homotopy
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- by Stephen Smale
- Proc. Amer. Math. Soc. 8 (1957), 604-610
- DOI: https://doi.org/10.1090/S0002-9939-1957-0087106-9
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References
- Edward G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. of Math. (2) 51 (1950), 534–543. MR 35015, DOI 10.2307/1969366 —, The Vietoris mapping theorem for bicompact spaces, II, Michigan Mathematical Journal vol. 3 (1956).
- Edward G. Begle, A fixed point theorem, Ann. of Math. (2) 51 (1950), 544–550. MR 35433, DOI 10.2307/1969367 W. Hurewicz, Homotopie, Homologie, und lokaler Zusammenhang, Fund. Math. vol. 25 (1935) pp. 467-485.
- Solomon Lefschetz, Topics in Topology, Annals of Mathematics Studies, No. 10, Princeton University Press, Princeton, N. J., 1942. MR 0007094
- M. H. A. Newman, Local connection in locally compact spaces, Proc. Amer. Math. Soc. 1 (1950), 44–53. MR 33530, DOI 10.1090/S0002-9939-1950-0033530-3
- Stephen Smale, A note on open maps, Proc. Amer. Math. Soc. 8 (1957), 391–393. MR 86295, DOI 10.1090/S0002-9939-1957-0086295-X
- L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann. 97 (1927), no. 1, 454–472 (German). MR 1512371, DOI 10.1007/BF01447877 R. L. Wilder, Mappings of manifolds, Summer Institute on Set Theoretic Topology, Madison, 1955. —, Some mapping theorems with applications to non-locally connected spaces, Algebraic Geometry and Topology, Princeton, 1956.
Bibliographic Information
- © Copyright 1957 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 8 (1957), 604-610
- MSC: Primary 55.0X
- DOI: https://doi.org/10.1090/S0002-9939-1957-0087106-9
- MathSciNet review: 0087106