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MATHEMATICA BOHEMICA, Vol. 123, No. 4, pp. 411-418 (1998)
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#
Disjoint sequences in Boolean algebras

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Jan Jakubik

* Jan Jakubik*, Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail: ` musavke@mail.saske.sk`

**Abstract:** 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.

**Keywords:** Boolean algebra, sequential convergence, disjoint sequence

**Classification (MSC2000):** 06E99, 11B99

**Full text of the article:**

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