Introduction to Topology

The aim of the book is to introduce the reader to the main chapters of the theory of metric spaces. At the beginning, in Chapter 1, concepts and propositions of analysis related to the convergence of sequences of real numbers and the continuity of real functions of a real variable are generalized to the Euclidean space ^IRn. This generalization is then made to metric spaces, i.e. spaces which are equipped, like Euclidean spaces, with some distance. The last chapter defines the notion of topology on a random set (without the presence of distance being necessary) and puts most of the concepts studied in the previous chapters back into a more general context.

Our ambition is not to make a simple record of knowledge but to achieve the deepest possible understanding of topological concepts, to become familiar with the methodology of dealing with topological problems and to provide stimuli for further study.