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Reduced coproducts of compact Hausdorff spaces

Published online by Cambridge University Press:  12 March 2014

Paul Bankston
Paul Bankston*
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53233
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Abstract

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the “reduced coproduct”, which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the “ultracoproduct” can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces.

Keywords

Reduced coproductscompactificationsreduced productscompact Hausdorff spacescategories
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 2 , June 1987 , pp. 404 - 424
Copyright
Copyright © Association for Symbolic Logic 1987

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