Generalized topologies induced by monotonic maps and hereditary classes

Abstract

It is shown in [3] that every generalized topology can be extended to a new one by using hereditary classes, called a generalized topology via a hereditary class. Following [5], the continuity on generalized topological spaces via hereditary classes was studied. In this thesis, we introduce the notion of generalized topological spaces induced by monotonic maps and hereditary classes and provide some of their properties. Also, we define and study the continuity on generalized topological spaces induced by monotonic maps and hereditary classes in various situations. Finally, we study some properties and characterizations of generalized topological spaces induced by monotonic maps having special properties and hereditary classes.