Topological and Metric Spaces

Abstract

It is natural to assume that any reader, who is familiar with any aspect of the theory of Ordinary Differential Equations, has already mastered basic topological notions as ‘open set’, ‘closure’, ‘closed set’, ‘continuous mapping’ (‘continuous function’), etc.. But aiming here to simplify our later account, we recall in this chapter some of these notions and related theorems We omit here proofs of theorems which may be assumed known by any reader who has a minimal training, except theorems which are based on arguments that illustrate well notions under consideration and relations between them. In order that the omissions of proofs do not make real difficulties in comprehension of the material we give references to books [Al] and [En], but these cases concern well known facts and the reader may use with about the same success other sources as textbooks on Mathematical or Functional Analysis. Lastly, he can consider the restoration of omitted proofs as an exercise within his powers (after some basic teaching).