Homotopical complexity and good spaces

Intermont, M.; Strom, J.

doi:10.1090/S0002-9947-06-03890-6

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.

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