Basic Algebraic Topology

Chapter 2 Cell Complexes and Simplicial Complexes

In this chapter we shall introduce two important classes of topological spaces. To begin with, by an open (closed) n-cell we mean a topological space which is homeomorphic to the open (closed) unit disc in ℝⁿ. Being contractible, these are among the simplest objects from the point of view of algebraic topology. On the other hand, from the point of view of differential topology, they are among the richest objects. The interior of these objects, viz., the open cells are the building blocks for manifolds and manifolds are the most suitable objects on which we can do calculus. The closed cells are going to be the building blocks for a large class of topological spaces called cell complexes, though ...