250044 VO Introduction to topology (2011S)

In this lecture (forming a non-separable unit together with the corresponding tutorials 250045), the basic notions of set-theoretic topology will be presented. We will build upon the relevant pre-knowledge from the lectures on analysis of one and several (real) variables where convergence, continuity, open and closed sets as well as compactness have already played a prominent rôle. The general frame for notions like these, being the basis of indispensable tools in nearly every field of mathematics, is provided by (metric and) topological spaces. The content of the lecture is centered around the core notions TC^3 (sometimes also TC^4: topology; [convergence,] continuity, compactness, connectedness). Of course, also metric spaces will receive due attention, as a source of examples for the general case of topological spaces and, moreover, with respect to their specific features.