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# When is the Natural Map $X \rightarrow \Omega\SigmaX$ a Cofibration?

L. Gaunce Lewis, Jr.
Transactions of the American Mathematical Society
Vol. 273, No. 1 (Sep., 1982), pp. 147-155
DOI: 10.2307/1999197
Stable URL: http://www.jstor.org/stable/1999197
Page Count: 9
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## Abstract

It is shown that a map $f: X \rightarrow F(A, W)$ is a cofibration if its adjoint $f: X \bigwedge A \rightarrow W$ is a cofibration and $X$ and $A$ are locally equiconnected (LEC) based spaces with $A$ compact and nontrivial. Thus, the suspension map $\eta: X \rightarrow \Omega\SigmaX$ is a cofibration if $X$ is LEC. Also included is a new, simpler proof that C. W. complexes are LEC. Equivariant generalizations of these results are described.

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