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Homotopical complexity and good spaces

Author(s): M. Intermont; J. Strom
Journal: Trans. Amer. Math. Soc. 359 (2007), 687-700.
MSC (2000): Primary 55Q05
Posted: August 16, 2006
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Abstract: This paper is an exploration of two ideas in the study of closed classes: the $ A$-complexity of a space $ X$ and the notion of good spaces (spaces $ A$ for which $ \mathcal{C}(A) = \overline{\mathcal{C}(A)}$). A variety of formulae for the computation of complexity are given, along with some calculations. Good spaces are characterized in terms of the functors $ CW_A$ and $ P_A$. The main result is a countable upper bound for $ \Sigma A$-complexity when $ A$ is a good space.

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Additional Information:

M. Intermont
Affiliation: Department of Mathematics, Kalamazoo College, Kalamazoo, Michigan 49006
Email: intermon@kzoo.edu

J. Strom
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
Email: Jeff.Strom@wmich.edu

DOI: 10.1090/S0002-9947-06-03890-6
PII: S 0002-9947(06)03890-6
Keywords: Closed class, complexity, homotopy colimit
Received by editor(s): June 10, 2004
Received by editor(s) in revised form: November 23, 2004
Posted: August 16, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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