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Cellular generators
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Cellular generators
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Journal Article
Cellular generators
2004
Overview
The aim of this paper is twofold. On the one hand, we show that the kernel C(A)¯\\overline {C(A)} of the Bousfield periodization functor PAP_A is cellularly generated by a space BB, i.e., we construct a space BB such that the smallest closed class C(B)C(B) containing BB is exactly C(A)¯\\overline {C(A)}. On the other hand, we show that the partial order (Spaces,≫)(Spaces,\\gg ) is a complete lattice, where B≫AB\\gg A if B∈C(A)B\\in C(A). Finally, as a corollary we obtain Bousfield’s theorem, which states that (Spaces,>)(Spaces,>) is a complete lattice, where B>AB>A if B∈C(A)¯B\\in \\overline {C(A)}.
Publisher
American Mathematical Society
