Topological Spaces

This chapter introduces the concept of topological space, the primary mathematical object in this book. The notion will appear devoid of any idea related to vicinity or nearness. A topological space is a set together with a collection of subsets endowed with some properties on the union and the intersection of its elements. Different equivalent ways to define a topological space will be established in the chapter, introducing the concepts of closed sets and bases. Finally, we address the concept of topological subspace.