Definition:Closed Linear Subspace

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Definition

Let $V$ be a topological vector space.

A linear subspace of $V$ that is closed is called a closed linear subspace.

Also see

• Definition:Vector Subspace
• Definition:Closed Linear Span, a commonly encountered closed linear subspace

• Closed Linear Subspaces Closed under Intersection
• Closed Linear Subspaces Closed under Setwise Addition