# Closed subset

From Topospaces

*This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces*

*A subset of a topological space has this property in the space iff its set-theoretic complement in the whole space is a/an:* open subset

This article is about a basic definition in topology.VIEW: Definitions built on this | Facts about this | Survey articles about this

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## Definition

A subset of a topological space is termed **closed** if it satisfies the following equivalent conditions:

- Its set-theoretic complement is an open subset
- It contains all its limit points