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In geometry, topology, and related branches of mathematics, a **closed set** is a set whose complement is an open set.^{[1]}^{[2]} In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation.
This should not be confused with a closed manifold.

**^**Rudin, Walter (1976).*Principles of Mathematical Analysis*. McGraw-Hill. ISBN 0-07-054235-X.**^**Munkres, James R. (2000).*Topology*(2nd ed.). Prentice Hall. ISBN 0-13-181629-2.