On inverse limits of homotopy sets
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- by Peter J. Kahn PDF
- Proc. Amer. Math. Soc. 47 (1975), 487-490 Request permission
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
- J. F. Adams, A variant of E. H. Brown’s representability theorem, Topology 10 (1971), 185–198. MR 283788, DOI 10.1016/0040-9383(71)90003-6 A. Deleanu, Remark on the Brown-Adams representability theorem, Syracuse University, 1971 (mimeo). P. J. Kahn, Brown’s representability theorem for compact functors, Cornell University, Ithaca, N. Y., 1972 (mimeo).
- J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337–341. MR 159327
- Dennis Sullivan, Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. Localization, periodicity, and Galois symmetry; Revised version. MR 0494074
Additional Information
- © Copyright 1975 American Mathematical Society
- 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