Topological aspects of continuity via generalized limit

Abstract


 
 
 This article aims to introduce the concept of generalized continuity of an function with respect to another function and to analyze the topological aspects of this concept Initially, the article presents the concept and the properties of generalized limit ofan function with respect to another function, highlighting that the Riemann integral is a particular case of generalized limit. Then, the definition of generalized continuity is presented, evidencing that this concept does not coincide with the classical continuity, being the last one a particular case of the first. Finally, some topological aspects associated with the concept of generalized continuity are approached in order to present proofs about the preservation of topological invariants via generalized continuity, such as preservation of compactness and connectedness.