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Saturated boolean algebras and their stone spaces

By Alan Dow

Abstract

AbstractFor an infinite cardinal κ, we call a compact zero-dimensional space a κ-Parovicenko space if its boolean algebra of clopen sets is κ-saturated and has cardinality κ<κ. We answer some questions about these spaces which were posed in [14]. For instance, it is shown that a κ+-Parovicenko spacé can be a Stone-Cech remainder in a natural way. We show that some of the results in [14] which used the assumption κ<κ=κ, do indeed require this assumption. We also show that if 2κ=κ+ then each compact Fκ+-space with weight κ+ can be embedded into a κ+-Parovicenko space (and so into an extremally disconnected space)

Publisher: Published by Elsevier B.V.
Year: 1985
DOI identifier: 10.1016/0166-8641(85)90104-X
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