Abstract
It is well known that the distance function or metric defined on a metric space
X induces a topology on that space X. Thus every metric space is a topological
space. In this project, we study how it is possible to reverse that statement. We
present some important criteria, which are necessary and sufficient, that topolog
ical spaces must possess in order to be metrizable. Applications of metrization
theorems to Moore spaces and manifolds are given.