Ohkawa's theorem: There is a set of Bousfield classes

Authors:
William G. Dwyer and John H. Palmieri

Journal:
Proc. Amer. Math. Soc. **129** (2001), 881-886

MSC (2000):
Primary 55P42, 55P60, 55U35

Published electronically:
September 20, 2000

MathSciNet review:
1712921

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**1.**A. K. Bousfield,*The Boolean algebra of spectra*, Comment. Math. Helv.**54**(1979), no. 3, 368–377. MR**543337**, 10.1007/BF02566281**2.**A. K. Bousfield,*The localization of spectra with respect to homology*, Topology**18**(1979), no. 4, 257–281. MR**551009**, 10.1016/0040-9383(79)90018-1**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.**Mark Hovey, John H. Palmieri, and Neil P. Strickland,*Axiomatic stable homotopy theory*, Mem. Amer. Math. Soc.**128**(1997), no. 610, x+114. MR**1388895**, 10.1090/memo/0610**5.**Tetsusuke Ohkawa,*The injective hull of homotopy types with respect to generalized homology functors*, Hiroshima Math. J.**19**(1989), no. 3, 631–639. MR**1035147**

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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:
https://doi.org/10.1090/S0002-9939-00-05669-0

Received by editor(s):
May 12, 1999

Published electronically:
September 20, 2000

Additional Notes:
This work was partially supported by the National Science Foundation, Grant DMS98-02386.

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2000
American Mathematical Society