1. Introduction. Among commutative rings, Boolean algebras stand just below fields in simplicity of structure. In contrast, little is known concerning their classification. The purpose of this paper is to present a decomposition theorem for complete Boolean algebras, which, in a small way, simplifies the classification problem. As an illustration of how this decomposition theorem can be used, i...

$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...