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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
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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
