The aim of our thesis is the extension of certain notions and results in functional analysis to non-metric topological spaces, in other words structures without distance. For this, we introduce a non-metric structure richer than the topological structure, for example: the uniform topology, and especially the spaces endowed with a family of semi-norms. At present, as applications of the fixed point theory, the most considered are the fixed point theorems of monotonic function in ordered Banach spaces.