A Vietoris mapping theorem for homotopy

Smale, Stephen

doi:10.1090/S0002-9939-1957-0087106-9

A Vietoris mapping theorem for homotopy

Author: Stephen Smale
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
Full-text PDF Free Access

Edward G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. of Math. (2) 51 (1950), 534–543. MR 35015, DOI https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/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.