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convergence $\ell $-group; disjoint subset; direct product; lexico extension; sequential convergence
In this paper we deal with the relation \[ \lim _\alpha \lim _\alpha X=\lim _\alpha X \] for a subset $X$ of $G$, where $G$ is an $\ell $-group and $\alpha $ is a sequential convergence on $G$.
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