In this paper, stratified L-ordered filter spaces and stratified L-ordered Cauchy spaces are introduced. It is shown that the category of stratified L-ordered filter spaces is a strongly Cartesian closed topological category and the category of stratified L-ordered Cauchy spaces is a Cartesian closed topological category. Also, the relationships among stratified L-ordered filter spaces, stratified L-ordered Cauchy spaces, stratified L-filter spaces and stratified L-Cauchy spaces are investigated.
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Bin Pang (2017) studied this question.
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