query: Subspace of metrizable and separable space is separable
positive_passages.docid: 22295
positive_passages.text: Subspace of a separable space is separable
negative_passages.docid: 49438
negative_passages.text: Prove that $X^\ast$ separable implies $X$ separable
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 97621
negative_passages.text: Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$
negative_passages.docid: 150720
negative_passages.text: Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
negative_passages.docid: 38516
negative_passages.text: Show a subset is subspace of a vectorspace and find the dimension
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 92291
negative_passages.text: $U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
negative_passages.docid: 4717
negative_passages.text: The union of linear subspaces is not necessarily a subspace
negative_passages.docid: 50946
negative_passages.text: Separable Hilbert space have a countable orthonormal basis
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 66550
negative_passages.text: Cardinality of separable metric spaces
negative_passages.docid: 70017
negative_passages.text: Every subspace of a compact space is compact?
negative_passages.docid: 127522
negative_passages.text: Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable
negative_passages.docid: 69206
negative_passages.text: A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
negative_passages.docid: 92774
negative_passages.text: Prove that a linear subspace of $C([0,1])$ is closed