<p> In this thesis we study extensive subcategories of various categories of Hausdorff spaces and continuous maps, and of Hausdorff uniform spaces and uniformly continuous maps, In particular, we obtain new methods to construct extensive subcategories which can be applied to many categories and give us an inclusive relationship between reflective subcategories of Haus and coreflective subcategories of Top. We consider perfect onto projectivity in those categories. The relationships between n-compact spaces and topologically complete spaces are discussed. </p> / Thesis / Doctor of Philosophy (PhD)