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The idea for injective hull of a metric space was introduced by Isbell. In [6] Isbell showed that every metric space X has an injective hull TX which is compact if X is compact. Dress [3] presented also examine the idea of the tight extension of a metric space. It is known that Dress’s theory is equivalent to the theory of the injective hull of a metric space independently discussed by Isbell some years earlier. Since one of the most interesting concepts in the theory of hyperconvex metric spaces is the notion of the injective hull of a metric space [5], it is very natural to wonder about the existence of an injective hull in the field of generalized metric spaces. From that point forward a considerable measure from claiming worth of effort have been carried in regards to those hyperconvexity for nonexpansive mappings (see [ 2, 4, 7, 9]).

Structure of u- Injective Hull in Ultra-Quasi-Pseudo Metric Space