Cellular generators
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- by Wojciech Chachólski, Paul-Eugene Parent and Donald Stanley PDF
- Proc. Amer. Math. Soc. 132 (2004), 3397-3409 Request permission
Abstract:
The aim of this paper is twofold. On the one hand, we show that the kernel $\overline {C(A)}$ of the Bousfield periodization functor $P_A$ is cellularly generated by a space $B$, i.e., we construct a space $B$ such that the smallest closed class $C(B)$ containing $B$ is exactly $\overline {C(A)}$. On the other hand, we show that the partial order $(Spaces,\gg )$ is a complete lattice, where $B\gg A$ if $B\in C(A)$. Finally, as a corollary we obtain Bousfield’s theorem, which states that $(Spaces,>)$ is a complete lattice, where $B>A$ if $B\in \overline {C(A)}$.References
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Additional Information
- Wojciech Chachólski
- Affiliation: Yale University, Department of Mathematics, 10 Hillhouse Avenue, P.O. Box 208283, New Haven, Connecticut 06520-8283
- Address at time of publication: KTH Matematik, S-10044 Stockholm, Sweden
- Email: chachols@math.yale.edu
- Paul-Eugene Parent
- Affiliation: Université catholique de Louvain, Département de mathméatiques, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgique
- Address at time of publication: KTH Matematik, S-10044 Stockholm, Sweden
- Email: parent@agel.ucl.ac.be
- Donald Stanley
- Affiliation: University of Alberta, Department of Mathematical Sciences, 632 Central Academic Building, Edmonton, Alberta, T6G 2G1, Canada
- Address at time of publication: Department of Mathematics and Statistics, University of Regina, College West, 30714 Regina, Saskatchewan, Canada
- MR Author ID: 648490
- Email: stanley@math.ualberta.ca
- Received by editor(s): November 1, 2000
- Received by editor(s) in revised form: January 1, 2001
- Published electronically: June 16, 2004
- Additional Notes: The first author was partially supported by the NSF grant DMS-9803766
This work has been partly supported by the Volkswagenstiftung Oberwolfach - Communicated by: Paul Goerss
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3397-3409
- MSC (2000): Primary 55Q05
- DOI: https://doi.org/10.1090/S0002-9939-04-07346-0
- MathSciNet review: 2073317