Convexity structures in T0-quasi-metric spaces

The authors define and investigate convexity structures in the sense of Takahashi in T0T0-quasi-metric spaces. They prove that numerous important results about convexity structures in metric spaces can be generalized to the quasi-metric setting. They also show that the latter convexity structures naturally occur in asymmetrically normed real vector spaces and in q  -hyperconvex T0T0-quasi-metric spaces. In the T0T0-quasi-metric setting they explore various interesting additional conditions that convexity structures in the sense of Takahashi can satisfy.