To a Question on the Supercompactness of Ultrafilter Spaces

Abstract

The space of ultrafilters of a \(\pi\)-system endowed with the topology of Wallman type is considered. The question on the supercompactness of this space is investigated. For this, the enveloping space of maximal linked systems with the corresponding topology of Wallman type is used. Necessary and sufficient conditions for the coincidence of the set of all ultrafilters of the initial \(\pi\)-system and the set of all maximal linked systems for this \(\pi\)-system are obtained. Specific variants of wide sense measurable spaces with this coincidence property are given.