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.
MUSHAANDJA, ZECHARIAH and OTAFUDU, OLIVIER OLELA
"Quasi-metric trees and $q$-hyperconvex hulls,"
Turkish Journal of Mathematics: Vol. 41:
1, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss1/12