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When is the natural map $ X\rightarrow \Omega \Sigma X$ a cofibration?


Author: L. Gaunce Lewis
Journal: Trans. Amer. Math. Soc. 273 (1982), 147-155
MSC: Primary 55P05
DOI: https://doi.org/10.1090/S0002-9947-1982-0664034-8
MathSciNet review: 664034
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Abstract: It is shown that a map $ f:X \to F(A,W)$ is a cofibration if its adjoint $ f:X \wedge A \to 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 \to \Omega \sum X$ 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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0664034-8
Keywords: Cofibration, equivariant cofibration, suspension map, locally equiconnected space, LEC space, Lillig Union Theorem, Dyer-Eilenberg Adjunction Theorem, geometric realization
Article copyright: © Copyright 1982 American Mathematical Society

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