Some aspects of Isbell-convex quasi-metric spaces

Abstract

<p>We introduce and investigate the concept of geodesic bicombing in T<sub>0</sub>-quasi-metric spaces. We prove that any Isbell-convex T<sub>0</sub>-quasi-metric space admits a geodesic bicombing which satisfies the equivariance property. Additionally, we show that many results on geodesic bicombing hold in quasi-metric settings, provided that non symmetry in quasi-metric spaces holds.</p>