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Documento electrónico extraido de Interne

Reduced Coproducts of Compact Hausdorff Spaces

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

One Constructed Reading Self after Another (A Response to Thomas F. Merrill)

A response to Thomas F. Merrill's "The Language of Hell.

Realcompact subspaces of size ω1

AbstractWe show that every uncountable compact space has a realcompact subspace of size ω1, that if there are no S-spaces, then every uncountable Tychonoff space has a realcompact subspace of size ω1 and that Ostazewski's space has no uncountable realcompact subspace

Bounded Subsets and Weak Realcompactness Conditions

A subset A of X is bounded if every continuous real-valued function on X is bounded on A. A completely regular Hausdorff space X is said to have the bz-property if every bounded subset of X is contained in a bounded zero subset of X. In this paper, we study the bz-property and its relation to other well known topological properties. We also introduce some new topological properties, all weaker than realcompactness, that are related to the bz-property. The origin of the bz-property lies in a measure-theoretic problem. Mathematics Subject Classification (1991): 5450, 54F99, 54G20 Keywords: bounded set, zero set, (weak) bz-space, (weak) m-space, space of pseudo countable type, unbounded point, untractable point, special sets defined by functions, counterexamples, completely regular, study, Lie Quaestiones Mathematicae 24(2) 2001, 225-23

Almost∗^* realcompactness

summary:We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness