query: Compact subspace in the union of closed embeddings
positive_passages.docid: 73154
positive_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 145952
negative_passages.text: Example of a closed subspace of a Banach space which is not complemented?
negative_passages.docid: 130156
negative_passages.text: Image of the union and intersection of sets.
negative_passages.docid: 63697
negative_passages.text: connected subspaces need to lie in one separated component
negative_passages.docid: 139951
negative_passages.text: Direct Sum of vector subspaces
negative_passages.docid: 107000
negative_passages.text: Dimension of intersection of distinct subspaces
negative_passages.docid: 59273
negative_passages.text: Cartesian product of embeddings is embedding
negative_passages.docid: 53261
negative_passages.text: Show that Pn is an (n+1)-dimensional subspace
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 32420
negative_passages.text: A complete orthonormal system contained in a dense sub-space.
negative_passages.docid: 146146
negative_passages.text: Proof that a closed subset of a compact space is a compact space
negative_passages.docid: 49563
negative_passages.text: Cauchy nets in a metric space
negative_passages.docid: 148994
negative_passages.text: $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 11301
negative_passages.text: Union of two vector subspaces not a subspace?
negative_passages.docid: 97914
negative_passages.text: Contractive mapping on compact space
negative_passages.docid: 124786
negative_passages.text: Prove that V contains a subspace of each dimension