Closed subset

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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.
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Definition

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

Relation with other properties

Stronger properties

Weaker properties