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Exhaustive zero-convergence structures on Boolean algebras. (English) Zbl 0969.06011
The authors give necessary and sufficient conditions for a Boolean algebra to admit the largest possible sequential convergence structure. For the motivation and basic definitions of convergence structures see J. Jakubík’s papers [Czech. Math. J. 38(113), 520-530 (1988; Zbl 0668.54002); Math. Bohem. 123, 411-418 (1998; Zbl 0934.06017)]. Also, it is proved that for any Boolean algebra $$B$$ and any sequential convergence structure $$S$$ on $$B$$, the join $$S\vee OS$$ in the semilattice of all convergence structures on $$B$$ exists. Here $$OS$$ is the classical order convergence structure on $$B$$.

##### MSC:
 06E10 Chain conditions, complete algebras 03G05 Logical aspects of Boolean algebras
##### Keywords:
Boolean algebra; sequential convergence structure
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