On the ultra-quasi-tight extensions

Abstract

In their previous paper [4], Künzi and Olela Otafudu constructed the ultra-quasi-metric hull of a T0-ultra-quasi-metric space. In this article, we continue these studies by investigating the tightness and essentiality of extension maps in the category of ultra-quasi-metric spaces and nonexpansive maps. We show, for instance, that q-spherical completeness is preserved by a retraction map. Furthermore, we point out some categorical aspects of ultra-quasi-metrically injective hulls.