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A Version of Zabrodsky's Lemma
Proceedings of the American Mathematical Society
Vol. 126, No. 5 (May, 1998), pp. 1573-1578
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/118816
Page Count: 6
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Zabrodsky's Lemma says: Suppose given a fibrant space Y and a homotopy fiber sequence F → E → X with X connected. If the map Y = map(*, Y) → map(F, Y) which is induced by F → * is a weak equivalence, then map(X, Y) → map(E, Y) is a weak equivalence. This has been generalized by Bousfield. We improve on Bousefield's generalization and give some applications.
Proceedings of the American Mathematical Society © 1998 American Mathematical Society