Relationships between completeness of fuzzy quasi-uniform spaces

Abstract

<span class="fontstyle0">In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizing<br />the relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0</span><span class="fontstyle2">, </span><span class="fontstyle0">1]-quasi-uniformities,<br />we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationships<br />between the completeness of induced probabilistic quasi-uniform spaces and both completeness of induced classical<br />quasi-uniform spaces and induced Hutton [0</span><span class="fontstyle2">, </span><span class="fontstyle0">1]-quasi-uniform spaces.</span> <br /><br />