## Homotopical complexity and good spaces

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- by M. Intermont and J. Strom PDF
- Trans. Amer. Math. Soc.
**359**(2007), 687-700 Request permission

## 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.## References

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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
- Received by editor(s): June 10, 2004
- Received by editor(s) in revised form: November 23, 2004
- Published electronically: August 16, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**359**(2007), 687-700 - MSC (2000): Primary 55Q05
- DOI: https://doi.org/10.1090/S0002-9947-06-03890-6
- MathSciNet review: 2255193