On the ultra-quasi-tight extensions - Mukongo, Demco Kalusokoma; Otafudu, Olivier Olela; Toko, Wilson Bombe (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023)
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.
Keywords: Ultra-quasi-metric,ultra-quasi-tight; ultra-quasi-essential