Q-hyperconvex t0-quasi-metric spaces

In this thesis, firstly the concept of hyperconvexity in metric spaces is given and then the q-hyperconvexity theory, which is the generalization of the concept of hyperconvexity to T0-quasi-metric spaces, is studied. In the first part of the thesis, which consists of five parts, an introduction to the thesis was made by mentioning the main purpose and the basic ideas of the thesis. In the second part of the thesis, the basic properties of metric and T0-quasi-metric spaces that will be used in the third and fourth chapters are given. In the third chapter, the concepts of hyperconvex and injective metric spaces are given and it is shown that these two concepts are equivalent. In addition, various properties of the hyperconvex hull of a metric space are mentioned. In the fourth chapter, which constitutes the main idea of the thesis, the concept of q-hyperconvexity for quasi-metric spaces is given and the concept of q-hyperconvex hull of a T0-quasi-metric space is examined with the help of function pairs spaces. In the last part, the thesis is completed by presenting some results obtained in the thesis study.