On infinite sums of closed ideals in $F}-lattices

Abstract

The main result of the paper is that if $(I_n)$ is a sequence of closed ideals in an $F$-lattice $E$, then also $\sum_{n=1}^\infty I_n$, the set of all elements $x\in E$ of the form $x=\sum_n x_n$, where $x_n\in I_n$ for every $n$, is a closed ideal in $E$.