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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0370573-1
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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0370573-1
Keywords: Inverse limit, homotopy set
Article copyright: © Copyright 1975 American Mathematical Society