Convexity structures in T-0-quasi-metric spaces

Kuenzi H. A., YILDIZ F.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 200
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.topol.2015.12.009
  • Dergi Adı: TOPOLOGY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2-18
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.