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Two Term Conditions in π Exact Couples

Published online by Cambridge University Press:  20 November 2018

Micheal N. Dyer
Micheal N. Dyer*
Affiliation:
University of California at Los Angeles
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In achieving his celebrated results on the homology groups of fibre spaces, J. P. Serre used the exact couple of a fibring defined by J. Leray. One of his main tools was the so-called two-term condition on the E2 term of this exact couple, which, if satisfied, yielded exact sequences, such as those of Gysin and Wang (see (5), Chapter IX). H. Fédérer, in (3), defined an exact couple (X, F, v) on the mapping space M(X, Y) = {ƒ:X → Y|X, Y are spaces and ƒ is continuous} with the compact-open topology, where X is a locally finite CW complex and Y is arc-connected and n-simple for all n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1263 - 1288
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Barratt, M. G., Track groups I, II, Proc. London Math. Soc., 5 (1955), 71–106, 285-329.Google Scholar
2. Eilenberg, Samuel and Steenrod, Norman, Foundations of algebraic topology (Princeton, 1952).Google Scholar
3. Federer, Herbert, A study of function spaces by spectral sequences., Trans. Amer. Math. Soc., 82 (1956), 340–361.Google Scholar
4. Hilton, P. J. and Wilie, Shawn, Homology theory (Cambridge, 1960).Google Scholar
5. Hu, S. T., Homotopy theory (New York, 1959).Google Scholar
6. Hu, S. T., Structure of homotopy groups of mapping spaces, Amer. J. Math., 71 (1949), 574–586.Google Scholar
7. Lefschetz, Solomon, Introduction to topology (Princeton, 1949).Google Scholar
8. Thorn, René, L'Homologie des espaces fonctionnels, Coll. de Top. Alg., Bruxelles, 7 (1957), 29–39.Google Scholar