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Proceedings of the American Mathematical Society

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On inverse limits of homotopy sets

Author: Peter J. Kahn
Journal: Proc. Amer. Math. Soc. 47 (1975), 487-490
MSC: Primary 55E05
MathSciNet review: 0370573
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Abstract: An elementary proof is given that, under certain conditions on a space $ F$, the homotopy set $ [X,F]$ maps bijectively onto the inverse limit of homotopy sets determined by the finite subcomplexes of $ X$. The only other satisfactory proof known requires the Brown representability theorem.

References [Enhancements On Off] (What's this?)

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  • [2] A. Deleanu, Remark on the Brown-Adams representability theorem, Syracuse University, 1971 (mimeo).
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Keywords: Inverse limit, homotopy set
Article copyright: © Copyright 1975 American Mathematical Society

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