query: Closed convex subset in Hilbert space
positive_passages.docid: 17159
positive_passages.text: Proof of Closest Point Theorem in Hilbert Space
negative_passages.docid: 30423
negative_passages.text: interior points and convexity
negative_passages.docid: 5506
negative_passages.text: Perturbation property of Orthonormal basis for Hilbert space
negative_passages.docid: 43504
negative_passages.text: Proving the existence of a complement subspace $U' \subset V$.
negative_passages.docid: 156101
negative_passages.text: Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
negative_passages.docid: 123732
negative_passages.text: Proving that the maximum of two convex functions is also convex
negative_passages.docid: 82900
negative_passages.text: Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
negative_passages.docid: 55533
negative_passages.text: Tensor Product: Hilbert Spaces
negative_passages.docid: 116632
negative_passages.text: Gram-Schmidt in Hilbert space?
negative_passages.docid: 57943
negative_passages.text: If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
negative_passages.docid: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 92497
negative_passages.text: Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
negative_passages.docid: 50946
negative_passages.text: Separable Hilbert space have a countable orthonormal basis
negative_passages.docid: 86643
negative_passages.text: Convex function almost surely differentiable.
negative_passages.docid: 100257
negative_passages.text: Converse to Hilbert basis theorem
negative_passages.docid: 58988
negative_passages.text: Composition of convex function and affine function
negative_passages.docid: 121095
negative_passages.text: Is convex hull of a finite set of points in $\mathbb R^2$ closed?