Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion

Abstract

Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.

Keywords

• fuzzy topology
• pair τ-filter
• cuachy pair τ-filter
• τ-quasi-cauchy space
• τ-quasi-uniform space
• l-metric space