Ultra-Quasi-Metrically Tight Extensions of Ultra-Quasi-Metric Spaces

The concept of the tight extension of a metric space was introduced and studied by Dress. It is known that Dress theory is equivalent to the theory of the injective hull of a metric space independently discussed by Isbell some years earlier. Dress showed in particular that for a metric space X the tight extension TX is maximal among the tight extensions of X. In a previous work with P. Haihambo and H.-P. Künzi, we constructed the tight extension of a T0-quasi-metric space. In this paper, we continue these investigations by presenting a similar construction in the category of UQP-metric spaces and nonexpansive maps