Introduction Manifolds are spaces like the sphere which look locally like Euclidean space. They include familiar surfaces.
Cell complexes are spaces made of pieces which are part of Euclidean space, generalizing polyhedra.
These are the most classic spaces on which groups of transformations act. This is also the setting for knot theory. History See the article on Topology at St Andrews. There is however some semblance to the present topic among metric spaces . Simplicial complexes are essentially polyhedra .