Reduced Coproducts of Compact Hausdorff Spaces

Bankston, Paul

J. Symbolic Logic, Tome 52 (1987) no. 1, p. 404-424 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1987-06-14
Classification:  Reduced Coproducts,  compactifications,  reduced products,  compact Hausdorff spaces,  categories,  54B25,  54D30,  54D35,  54G05,  54G10,  54J05