# Pages that link to "Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset"

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The following pages link to **Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset**:

- For any vector subspace of a Hilbert space the orthogonal complement and the closure of that subspace form a direct sum of the entire space (← links)