query: The subspace sum of closed subspaces is closed
positive_passages.docid: 141762
positive_passages.text: The direct sum of two closed subspace is closed? (Hilbert space)
negative_passages.docid: 1475
negative_passages.text: In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
negative_passages.docid: 61316
negative_passages.text: Sum of closed spaces is not closed
negative_passages.docid: 74764
negative_passages.text: Dimension for a closed subspace of $C[0,1]$.
negative_passages.docid: 126897
negative_passages.text: Showing the set $A+B$ is closed.
negative_passages.docid: 127591
negative_passages.text: How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
negative_passages.docid: 33310
negative_passages.text: Proving that the set of limit points of a set is closed
negative_passages.docid: 145952
negative_passages.text: Example of a closed subspace of a Banach space which is not complemented?
negative_passages.docid: 157303
negative_passages.text: An operator has closed range if and only if the image of some closed subspace of finite codimension is closed.
negative_passages.docid: 95887
negative_passages.text: How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
negative_passages.docid: 98391
negative_passages.text: example of a nonempty subset is closed under scalar multiplication but not a subspace
negative_passages.docid: 53261
negative_passages.text: Show that Pn is an (n+1)-dimensional subspace
negative_passages.docid: 108740
negative_passages.text: $C^1[a,b]$ is closed in $C[a,b]$
negative_passages.docid: 4151
negative_passages.text: Every subspace of a vector space has a complement
negative_passages.docid: 42494
negative_passages.text: The boundary is a closed set
negative_passages.docid: 60684
negative_passages.text: Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
negative_passages.docid: 76160
negative_passages.text: Dimension of the sum of two vector subspaces