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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cellular generators


Authors: Wojciech Chachólski, Paul-Eugene Parent and Donald Stanley
Journal: Proc. Amer. Math. Soc. 132 (2004), 3397-3409
MSC (2000): Primary 55Q05
Published electronically: June 16, 2004
MathSciNet review: 2073317
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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 $B\in\overline{C(A)}$.


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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
Email: stanley@math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07346-0
PII: S 0002-9939(04)07346-0
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
Article copyright: © Copyright 2004 American Mathematical Society