N-Methods

OpenAlex · English

In this paper, we present the concept of GN-topological space by introducing a topology defined on a subfamily of the family consisting of all convergent nets in any general topological space. Inspired by the method concept, which is a type of function whose domain is a set of convergent sequences and whose range is a set of real numbers, we define a different type of function, which we call the N-method, whose range is a general topological space and whose domain is the GN-topological space defined on this topological space. After stating the elements that led us to conduct this research and the sources of inspiration for us, we examine the properties of some types of continuities on the concept of the N-method, whose basis is the concept of an h-open set, and reveal the relations between them. In the following section, we similarly introduce the nano GN-topological space and nano N-method concepts and examine the behaviors of the continuity types, which are based on the concept of the nano h-open set and nano N-method. In the conclusion, we outline the impact we expect our studies to have on the scientific world.