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Keywords:
Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice
Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice
Summary:
We deal with the system ${\operatorname{Conv}} B$ of all sequential convergences on a Boolean algebra $B$. We prove that if $\alpha$ is a sequential convergence on $B$ which is generated by a set of disjoint sequences and if $\beta$ is any element of ${\operatorname{Conv}} B$, then the join $\alpha\vee\beta$ exists in the partially ordered set ${\operatorname{Conv}} B$. Further we show that each interval of ${\operatorname{Conv}} B$ is a Brouwerian lattice.
References:
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