Intrinsic metric spaces

In this thesis, intrinsic metric spaces and the notions of hyperconvexity, injectivity, tight span are investigated. Properties of intrinsic metric spaces and strictly intrinsic metric spaces are investigated. It is defined the notion of uniquely geodesic space and discussed under what conditions the product of two uniquely geodesic metric spaces is also uniquely geodesic space. Geodesic segment on R^n associated with the metrics d_1 and d_∞ are characterized. Then the notions of injectivity, hyperconvexity and tight span are defined and relationships between these notions are studied. Tight span of a subset of (R^2, d_∞) is examined isometrically and it is seen that this characterization can not be generalized to (R^n, d_∞).