Transactions of the American Mathematical Society

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



A continuous localization and completion

Author: Norio Iwase
Journal: Trans. Amer. Math. Soc. 320 (1990), 77-90
MSC: Primary 55P60; Secondary 55N91, 55P20, 55U40
MathSciNet review: 1031978
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Abstract: The main goal of this paper is to construct a localization and completion of Bousfield-Kan type as a continuous functor for a virtually nilpotent CW-complex. Then the localization and completion of an $ {A_n}$-space is given to be an $ {A_n}$-homomorphism between $ {A_n}$-spaces. For any general compact Lie group, this gives a continuous equivariant localization and completion for a virtually nilpotent $ G$-CW-complex. More generally, we have a continuous localization with respect to a system of core rings for a virtually nilpotent $ \mathbf{D}$-CW-complex for a polyhedral category $ \mathbf{D}$.

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Keywords: Localization, completion, continuous functor, higher homotopy associativity, $ G$-space, $ \mathbf{D}$-space
Article copyright: © Copyright 1990 American Mathematical Society