Some aspects of Isbell-convex quasi-metric spaces


  • Olivier Olela Otafudu University of the Witwatersrand



Isbell-convexity, geodesic bicombing, injectivity


We introduce and investigate the concept of geodesic bicombing in T0-quasi-metric spaces. We prove that any Isbell-convex T0-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.


Download data is not yet available.

Author Biography

Olivier Olela Otafudu, University of the Witwatersrand

School of Mathematics


C. A. Agyingi, P. Haihambo and H.-P. A. Künzi, Tight extensions of T0-quasi-metric spaces, Logic, computation, hierarchies, Ontos Math. Log., 4, De Gruyter, Berlin, 2014, pp 9-22.

G. Berthiaume, On quasi-uniformities in hyperspaces, Proc. Amer. Math. Soc. 66 (1977), 335-343.

J. Conradie, H.-P. A. ünzi and O. Olela Otafudu, The vector lattice structure on the Isbell-convex hull of an asymmetrically normed real vector space, Topology Appl. 231 (2017), 92-112.

D. Descombes and U. Lang, Convex geodesic bicombings and hyperbolicity, Geom. Dedicata 177 (2015), 367-384.

A. W. M. Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. Math. 53 (1984), 321-402.

J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964), 65-76.

E. Kemajou, H.-P.A. Künzi and O. Olela Otafudu, The Isbell-hull of a di-space, Topology Appl. 159 (2012), 2463-2475.

H.-P. A. Künzi and C. Ryser, The Bourbaki quasi-uniformity, Topology Proc. 20 (1995), 161-183.

H.-P. A. Künzi and F. Yildiz, Convexity structures in T_0-quasi-metric spaces, Topology Appl. 200 (2016), 2-18.

U. Lang. Injective hulls of certain discrete metric spaces and groups. J. Topol. Anal. 5 (2013) 297-331.

O. Olela Otafudu and Z. Mushaandja, Versatile asymmetrical tight extensions, Topol. Algebra Appl. 5 (2017), 6-12




How to Cite

O. Olela Otafudu, “Some aspects of Isbell-convex quasi-metric spaces”, Appl. Gen. Topol., vol. 19, no. 1, pp. 173–187, Apr. 2018.



Regular Articles