On fuzzy pseudo-metric spaces

This paper attempts to endow the fuzzy pseudo-metric in the sense of George and Veeramani with many-valued topological structures. It is shown that George and Veeramaniʹs fuzzy pseudo-metric can be characterized by a family of compatible ordinary pseudo-metrics called pseudo-metric chain in this paper. Then, two kinds of many-valued topological structures—fuzzifying topology and fuzzifying uniformity—are generated by this fuzzy pseudo-metric, and their properties are also investigated.