Geodesic
Disjoint sequences in Boolean algebras
Mathematica Bohemica, Tome 123 (1998) no. 4, pp. 411-418
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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.
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.
DOI : 10.21136/MB.1998.125963
Classification : 06A12, 06E05, 06E99, 11B99
Keywords: Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice 
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Jakubík, Ján. Disjoint sequences in Boolean algebras. Mathematica Bohemica, Tome 123 (1998) no. 4, pp. 411-418. doi: 10.21136/MB.1998.125963

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