Topological Essence of the Concept “Limit of a Function” in the General Mathematics

Abstract

The limit of a function is one of the most important concepts in high school mathematics. But unfortunately, not many students understand the essence of this concept. They had to accept it. This paper presents the topological essence of a limit of a function and discusses methods for teaching this concept in general education in Viet Nam. It consists of four parts. Part 1 talks about the definition of “Limit of a function”, part 2 covers the Mathematical essence of the concept limit of a function, part 3 deals with Defining the limit of a function in a topological space of real numbers and part 4 presents Adding a topology on the set of real numbers and limit of a function. In each section, we include comments to help teach these notions and concepts.