Quasi-metric trees and $q$-hyperconvex hulls

Authors: ZECHARIAH MUSHAANDJA, OLIVIER OLELA OTAFUDU

Abstract: The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the $q$-hyperconvex hull of a $q$-hyperconvex $T_0$-quasi-metric tree is itself a $T_0$-quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.

Keywords: Metric interval, metric tree, $T_0$-quasi-metric, quasi-metric interval, quasi-metric tree

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