Often working in certain areas of mathematics and its applications in other branches of science, fortified building objects from universal properties of given objects. These ideas motivate the definitions of coreflective and reflective subcategories, expressing notions improvement, optimization and density. In this article we review the theory of reflective and coreflective subcategories of the category of topological spaces and proposes new methods of construction of these categories in the category of topological spaces and in the category of topological spaces with base point