CW complex

Summary

A CW complex is a space built by gluing closed balls of increasing dimension, called cells. Each ball is glued along its boundary sphere to the cells already present. The class of CW complexes is flexible enough to contain spheres, projective spaces, Grassmannians, all simplicial complexes and, up to homotopy equivalence, all manifolds. It is rigid enough for homotopy theory to work well. Weak homotopy equivalences between CW complexes are homotopy equivalences, and homology can be computed cell by cell. The letters C and W stand for closure-finite and weak topology, the two conditions of J. H. C. Whitehead's definition.