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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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