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A version of Zabrodsky's lemma

Author: Jin-yen Tai
Journal: Proc. Amer. Math. Soc. 126 (1998), 1573-1578
MSC (1991): Primary 55P60
MathSciNet review: 1443169
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Abstract: Zabrodsky's Lemma says: Suppose given a fibrant space $Y$ and a homotopy fiber sequence $F\to E\to X$ with $X$ connected. If the map $Y=\operatorname {map}(*,Y)\to \operatorname {map}(F,Y) $ which is induced by $F\to *$ is a weak equivalence, then $\operatorname {map}(X,Y)\to \operatorname {map}(E,Y)$ is a weak equivalence. This has been generalized by Bousfield. We improve on Bousfield's generalization and give some applications.

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Jin-yen Tai
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755

Received by editor(s): April 11, 1996
Received by editor(s) in revised form: October 30, 1996
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society