Algebraic Topology: A Computational Approach

To read this book you do not need to have studied general topology.
The subject of Topology grew out of the foundations of calculus and more generally analysis. If you took a typical calculus sequence, then you began by learning about functions of the real line. The focus was on dierentiable functions and how they can be best approximated locally by linear functions (the derivative). Along the way you learned about continuous functions. Again, the emphasis was on local properties such as limits a notable exception is the intermediate value theorem. Later on these concepts were generalized to functions of more than one variable, i.e. functions from Rn to Rm. Topology incorporates further generalizations. In particular, it allows one to study the local and global properties of continuous functions between general spaces.