Stratified <i>L</i>-ordered filter spaces

Abstract

In this paper, stratied L-ordered filter spaces and stratied L-ordered Cauchy spaces are introduced. It is shown that the category of stratied L-ordered filter spaces is a strongly Cartesian closed topological category and the category of stratied L-ordered Cauchy spaces is a Cartesian closed topological category. Also, the relationships among stratied L-ordered filter spaces, stratified L-ordered Cauchy spaces, stratied L-filter spaces and stratied L-Cauchy spaces are investigated.

Keywords: (Stratied) L-ordered filter space, (stratied) L-ordered Cauchy space, fuzzy order, (strongly) Cartesian closed