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Ohkawa's theorem: There is a set of Bousfield classes
Author(s):
William
G.
Dwyer;
John
H.
Palmieri
Journal:
Proc. Amer. Math. Soc.
129
(2001),
881-886.
MSC (2000):
Primary 55P42, 55P60, 55U35
Posted:
September 20, 2000
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Abstract:
We give a simple proof of Ohkawa's theorem, that there is a set of Bousfield classes. The proof leads us to consider the partially ordered set of Ohkawa classes, especially as it compares to the partially ordered set of Bousfield classes.
References:
-
- 1.
- A. K. Bousfield, The Boolean algebra of spectra, Comment. Math. Helv. 54 (1979), no. 3, 368-377. MR 81a:55015
- 2.
- -, The localization of spectra with respect to homology, Topology 18 (1979), no. 4, 257-281. MR 80m:55006
- 3.
- M. Hovey and J. H. Palmieri, The structure of the Bousfield lattice, Homotopy invariant algebraic structures (J.-P. Meyer, J. Morava, and W. S. Wilson, eds.), Contemp. Math., vol. 239, Amer. Math. Soc., Providence, RI, 1999.
- 4.
- M. Hovey, J. H. Palmieri, and N. P. Strickland, Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 128 (1997), no. 610, x+114. MR 98a:55017
- 5.
- T. Ohkawa, The injective hull of homotopy types with respect to generalized homology functors, Hiroshima Math. J. 19 (1989), no. 3, 631-639. MR 90j:55013
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Additional Information:
William
G.
Dwyer
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
dwyer.1@nd.edu
John
H.
Palmieri
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email:
palmieri@member.ams.org
DOI:
10.1090/S0002-9939-00-05669-0
PII:
S 0002-9939(00)05669-0
Received by editor(s):
May 12, 1999
Posted:
September 20, 2000
Additional Notes:
This work was partially supported by the National Science Foundation, Grant DMS98-02386.
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
2000,
American Mathematical Society
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