Round-Up of Topology

Abstract

The concepts of topology and of topological space took shape in the mid 1800s with the study of \(\mathbb {R}\) and more generally Euclidean space, together with the properties of continuous maps on such spaces. Associated to the notion of topological space is the primitive concept of open set, from which the concept of neighbourhood descends, and then closed sets, closure, interior, frontier and boundary points, limit points and isolated points, etc.. The purpose of this Chapter is to present this preliminary matter.