Closed manifold

A closed manifold is a compact topological manifold without boundary. If a manifold without boundary is defined in the context, is a compact manifold automatically closed.

The simplest example is a circuit with the induced open canonical topology. This is a compact one-dimensional manifold without boundary. Other examples of closed manifolds are the sphere, the projective plane, the Klein bottle and the torus.

Compared example, the real line, since it is not compact and the two-dimensional circular disk. The latter is compact but has a margin.

The concept of closed manifold must not be confused with the notion of a closed set. ( The latter is defined subsets of a topological space, relative to the topology of the room. ) To any of the sub- manifold is automatically completed, as the above examples illustrate, but do not necessarily closed.

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