Topological properties of L-partial pseudo-quasi- metric spaces

As an application of partial metrics and fuzzy set theory, the concept of L-partial pseudo-quasi-metric spaces is introduced and its topological properties are investigated. It is shown that L-partial pseudo-quasi- metrics are reasonable generalizations of partial pseudo-quasi-metrics and pointwise metrics in the sense of Shi. Also, it is proved that an L-partial pseudo-quasi-metric space can be endowed with an L-cotopology and a pointwise quasi-uniformity. Moreover, an L-partial pseudo-quasi-metric and its induced pointwise quasi-uniformity induce the same L-cotopology.