Compactly Generated Spaces and Quasi-spaces in Topology

摘要

The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category Top of topological spaces and continuous functions, to study compactly generated spaces and quasi-spaces in this setting. Moreover, for a class C of objectswe generalize the notion of C-generated spaces, fromwhich we derive, for instance, a general concept of Alexandroff spaces. Furthermore, as done for Top, we also study, in our level of generality, the relationship between compactly generated spaces and quasi-spaces.