Relationships between completeness of fuzzy quasi-uniform spaces

In this paper, we give a kind of Cauchy ۱-completeness in probabilistic quasi-uniform spaces by using ۱-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [۰, ۱]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced probabilistic quasi-uniform spaces and both completeness of induced classicalquasi-uniform spaces and induced Hutton [۰, ۱]-quasi-uniform spaces.

Keywords:

probabilistic quasi-uniformity , classical quasi-uniformity , Hutton [۰ , ۱]-quasi-uniformity , ۱-filter , Cauchy ۱-completeness