Lyall Reid - Department of Mathematics, University of Central Florida, ۴۳۹۳ Andromeda Loop N, Orlando, FL ۳۲۸۱۶, United States
Gary Richardson - Department of Mathematics, University of Central Florida, ۴۳۹۳ Andromeda Loop N, Orlando, FL ۳۲۸۱۶, United States

\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.  Moreover, a  compactification of a \top-convergence space is constructed whenever L is a complete Boolean algebra.

Lattice-valued convergence, top-convergence spaces, Regularity, Compactification, Topological