A continuous localization and completion

Iwase, Norio

doi:10.1090/S0002-9947-1990-1031978-1

A continuous localization and completion
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Trans. Amer. Math. Soc. 320 (1990), 77-90 Request permission

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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