Cellular generators

Chacholski, W;Parent, PE;Stanley, D
(2004) Proceedings of the American Mathematical Society — Vol. 132, n° 11, p. 3397-3409 (2004)

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  • Chacholski, W
    Author
  • Parent, PE
    Author
  • Stanley, D
    Author
Abstract
The aim of this paper is twofold. On the one hand, we show that the kernel <(C(A))over bar> 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 C( A). On the other hand, we show that the partial order (Spaces, much greater than) is a complete lattice, where B much greater than A if B is an element of C(A). Finally, as a corollary we obtain Bousfield's theorem, which states that (Spaces, >) is a complete lattice, where B > A if B is an element of<(C(A))over bar>.
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Chacholski, W., Parent, P., & Stanley, D. (2004). Cellular generators. Proceedings of the American Mathematical Society, 132(11), 3397-3409. https://doi.org/10.1090/S0002-9939-04-07346-0 (Original work published 2004)