Convexity structures in T-0-quasi-metric spaces


Kuenzi H. A., YILDIZ F.

TOPOLOGY AND ITS APPLICATIONS, vol.200, pp.2-18, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 200
  • Publication Date: 2016
  • Doi Number: 10.1016/j.topol.2015.12.009
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2-18
  • Hacettepe University Affiliated: Yes

Abstract

The authors define and investigate convexity structures in the sense of Takahashi in T-0-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 T-0-quasi-metric spaces. In the T-0-quasi-metric setting they explore various interesting additional conditions that convexity structures in the sense of Takahashi can satisfy. (C) 2015 Elsevier B.V. All rights reserved.