A compact manifold is a manifold that is compact as a topological space. Examples are the circle (the only one-dimensional compact manifold) and the n-dimensional sphere and torus. Compact manifolds in two dimensions are completely classified by their orientation and the number of holes (genus). It should be noted that the term "compact manifold" often implies "manifold without boundary, " which is the sense in which it is used here. When there is need for a separate term, a compact boundaryless manifold is called a closed manifold.

closed manifold | compact space | manifold | sphere | topological space | torus | Tychonoff compactness theorem