The distance on a set is a comparative function. The smaller the distance
between two elements of that set, the closer, or more similar, those elements
are. Fr\'echet axiomatized the distance into what is today known as a metric.
In this thesis we study the generalization of Fr\'echet's axioms in various
ways including a partial metric, strong partial metric, partial
n−Metric and strong partial n−Metric. Those
generalizations allow for negative distances, non-zero distances between a
point and itself and even the comparison of n−tuples. We then present the
scoring of a DNA sequence, a comparative function that is not a metric but can
be modeled as a strong partial metric. Using the generalized metrics mentioned
above we create topological spaces and investigate convergence, limits and
continuity in them. As an application, we discuss contractiveness in the
language of our generalized metrics and present Banach-like fixed, common fixed
and coincidence point theorems.Comment: Thesi