Subcategories of the category of $\top$-convergence spaces

Abstract

$\top$-convergence structures serve as an important tool to describe fuzzy topology. This paper aims to give further investigations on $\top$-convergence structures. Firstly, several types of $\top$-convergence structures are introduced, including Kent $\top$-convergence structures, $\top$-limit structures and principal $\top$-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base" approach is applied to $\top$-convergence structures and the relationships between $\top$-convergence structures with respect to different underlying lattices are demonstrated.