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On Wallman Spaces and the Lindelöf Property
Author(s) -
EID GEORGE M.
Publication year - 1992
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1992.tb32247.x
Subject(s) - ultrafilter , countable set , mathematics , intersection (aeronautics) , lattice (music) , pure mathematics , property (philosophy) , finitely generated abelian group , filter (signal processing) , discrete mathematics , computer science , physics , philosophy , epistemology , acoustics , engineering , aerospace engineering , computer vision
It is assumed that X is an abstract set and ℒ is a lattice of subsets of X. The consequences of ℒ being regular, and of ℒ being regular together with other lattice properties such as prime complete or even Lindelöf, are discussed first. Next, the important problem of enlarging an ℒ‐filter or an ℒ‐ultrafilter with the countable intersection property is considered. It is much easier to express this in terms of zero–one‐valued finitely additive measures on the algebra generated by ℒ. Conditions for the preceding to hold in terms of topological spaces of measures associated with the lattice ℒ are then obtained.