The category of T-filter spaces

Abstract

T-filters serve as an important tool to define mathematical structures and deserve more and more attention. This paper aims to investigate categorical properties of T-filter spaces. Firstly, it is shown that the category T-Fil of T-fiter spaces is Cartesian closed, extensional and productive for quotient mappings.  Secondly, the concepts of T-semi-Cauchy spaces and complete T-filter spaces are proposed. It is proved that the categories of T-semi-Cauchy spaces and  T-Cauchy spaces, as bireflective subcategories of T-Fil, are Cartesian closed, and the category of complete T-filter spaces, as a bicoreflective subcategory of T-Fil, is strongly Cartesian closed and is isomorphic to that of symmetric Kent T-convergence spaces.