TL;DR
This paper characterizes specific semilattices that lead to Boolean spaces via their ultrafilters, highlighting the role of 0-disjunctive semilattices in inverse semigroup theory.
Contribution
It provides a characterization of semilattices that produce Boolean spaces, emphasizing the significance of 0-disjunctive semilattices in the context of inverse semigroups.
Findings
Identification of conditions for semilattices to generate Boolean spaces
Highlighting the importance of 0-disjunctive semilattices in the theory
Connection between semilattice properties and topological space structures
Abstract
We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished role in this theory.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · semigroups and automata theory