# Closed set

## Complement of an open subset / From Wikipedia, the free encyclopedia

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This article is about the complement of an open set. For a set closed under an operation, see closure (mathematics). For other uses, see Closed (disambiguation).

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.