Document Type: Research Paper


Department of Mathematics, University of Central Florida, 4393 Andromeda Loop N, Orlando, FL 32816, 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.


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