A topological space is one with enough structure for defining continuity. A topological manifold is intermediate between a topological space and a smooth manifold. A smooth manifold is one with enough structure for defining derivatives. The smooth manifold RN, the set of N-tuples of real numbers equipped with the standard smooth structure, is a familiar example from which all others can be constructed patchwise. This article is a brief reminder of the basic ideas. A list of relationships between various types of topological spaces is given at the end, summarized graphically by a Venn diagram.
