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In this thesis, we recall three types of convexities in metric spaces, namely; Menger convexity, Takahashi convexity andM-convexity. We then generalise these convexities to the framework of T0-quasi-metric spaces. Since the concept of convexities heavily relies on the concept of betweenness, a...

The concept of hyperconvexity in metric spaces was introduced by Aronszajn and Panichpakdi in 1956. This concept was then generalised to the framework of quasi-metric spaces by John Isbell in 1964, which he called Isbell convexity. In 2019, Yi git and Efe generalised this concept of...