Basic Algebraic Topology

Chapter 1 Introduction

We shall assume that the readers of this book have had a course in general point-set topology and are familiar with some basic notions such as connectedness, path connectedness, local path-connectedness, compactness, Hausdorffness, etc. Some of the slightly more advanced topics such as function spaces, quotient spaces, etc., will be recalled as a ready reference.

Throughout this exposition, we shall use the word ‘space’ to mean a topological space. Similarly, we shall use the word ‘map’ to mean a continuous function between topological spaces. This however, does not forbid us from using terminologies such as ‘linear map’ or ‘simplicial map’, etc., wherein we may not really be bothered about the function being continuous, ...