Investigation on the structure of lipschitz-free banach space

Abstract

In this dissertation we showed that, the Lipschitz-free space over a quasi-ultrametric space has monotone Schauder basis. Also we showed that, in a quasi-metric space, l_∞is linearly isomorphic to a subspace of the space of Lipschitz functions. Lastly, we showed that, Lipschitz-free space over a sequentially metric space contains a 1-complemented subspace isometric to l_1.