On Gluing of Quasi-Pseudometric Spaces

Document Type : Original Article

Authors

Yolanda Mutemwa ¹

Olivier Olela Otafudu ²

Hope Sabao ²

¹ School of Mathematical Sciences, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa.

² School of Mathematics, University of the Witwatersrand Johannesburg 2050, South Africa.

10.22034/kjm.2019.97193

Abstract

The concept of gluing a family of $T_0$-quasi-metric spaces along subsets was introduced by Otafudu. In this article, we continue the study of externally Isbell-convex and weakly externally Isbell-convex subsets of a $T_0$-quasi-metric space. We finally investigate some properties of the resulting $T_0$-quasi-metric space obtained by gluing a family of Isbell-convex $T_0$-quasi-metric spaces attached
along isometric subspaces.

Keywords

Isbell-convexity

gluing quasi-pseudometric

externally Isbell-convexity

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