Olela Otafudu, OlivierMutemwa, Ingutu Yolanda2021-03-012021-03-012020http://hdl.handle.net/10394/36824https://orcid.org/0000-0002-1962-8450Master (Mathematics), North-West University, Mafikeng Campus, 2017A classical problem that arises in geometry is how to glue a family of metric spaces such that the resulting space preserves their properties. In this MSc dissertation, we generalise the concept of gluing a family of metric spaces to the framework of quasi-pseudometric spaces. In particular, we will look at gluing a family of q-hyperconvex quasi-pseudo metric spaces along externally q-hyperconvex subsets and along weakly externally q-hyperconvex subsets such that the resulting space preserves the q-hyperconvexity structure. We relate these results to the well-known results in the literature. The notion of externally q-hyperconvex quasi-pseudometric spaces and weakly externally q-hyperconvex spaces are revisited and some original results are presented. Moreover, we introduce the concept of gated subsets of a quasi-pseudometric space and extend the notion of strong convexity in our context.enThesis