Basic Topology: a review

Abstract

In this section we briefly recall and collect some of the basic definitions and results of point set topology which will be needed later for explaining the concepts of algebraic topology. Important definitions are followed by some quick examples and, if necessary, by some comments. The results are mostly stated without proofs, but occasionally well-known proofs are indicated merely to highlight some important routine arguments. Emphasis has been laid mostly on those topics of set-topology which appear necessary for a correct understanding of subsequent chapters. We assume that the student is somewhat already familiar with the basic notions of set topology, particularly with quotient spaces, connectedness and compactness, etc., which are used here freely regardless of the order in which they occur in these preliminaries. Definitions and results can be referred back while reading the material of algebraic topology as and when they are required.