The category of stratified L-filter spaces

In this paper, the concepts of stratified L-filter space, complete stratified L-filter space and symmetric stratified L-Kent convergence space are introduced. It is shown that (1) the category of stratified L-filter spaces with Cauchy continuous maps is a strong topological universe; (2) the category of complete stratified L-filter spaces, as a bicoreflective subcategory of the category of stratified L-filter spaces, is isomorphic to the category of symmetric stratified L-Kent convergence spaces; (3) the category of complete stratified L-filter spaces, as an isomorphism-closed full subcategory of the category of stratified L-filter spaces, is strongly Cartesian closed.