Abstract
The material of this section is divided into four sub-sections dealing with Topology, the finitary properties of Boolean algebras, the duality of Stone between Boolean algebras and compact totally disconnected spaces, and the completion of a Boolean algebra and the (essentially dual) Gleason space of a compact space. Three spaces are involved: The Stone-Čech compactification of a space, the Stone space of a Boolean algebra, and the Stone space of the (complete) Boolean algebra of regular-open sets of a space. The definitions use either the topological version of an ultrafilter, namely a z-ultrafilter on a space, or the algebraic version of an ultrafilter, namely an ultrafilter of a Boolean algebra; these are (non-comparable) generalizations of the set-theoretic version of an ultrafilter, namely the ultrafilter on a cardinal number.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Comfort, W.W., Negrepontis, S. (1974). Topology and Boolean Algebras. In: The Theory of Ultrafilters. Die Grundlehren der mathematischen Wissenschaften, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65780-1_2
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DOI: https://doi.org/10.1007/978-3-642-65780-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65782-5
Online ISBN: 978-3-642-65780-1
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