query: A subspace of a separable space is not necessarily seperable
positive_passages.docid: 10034
positive_passages.text: Give an example of a non-separable subspace of a separable space
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 6547
negative_passages.text: Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
negative_passages.docid: 91173
negative_passages.text: Finite-dimensional subspace normed vector space is closed
negative_passages.docid: 50946
negative_passages.text: Separable Hilbert space have a countable orthonormal basis
negative_passages.docid: 63538
negative_passages.text: Impossibility of constructing a continuum-size linearly independent set in $\Bbb R$
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 110832
negative_passages.text: $F_\sigma$-subsets in a normal space can be separated
negative_passages.docid: 127419
negative_passages.text: Subspace of Noetherian space still Noetherian
negative_passages.docid: 95635
negative_passages.text: $\ell^{\infty}(\mathbb N)$ is not a separable space
negative_passages.docid: 19396
negative_passages.text: For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
negative_passages.docid: 53859
negative_passages.text: Continuous image of separable space
negative_passages.docid: 45111
negative_passages.text: Number of Subspaces that contains other Space
negative_passages.docid: 131890
negative_passages.text: Totally disconnected space that is not $T_2$
negative_passages.docid: 67191
negative_passages.text: When is the union of a family of subspaces of a vector space also a subspace?
negative_passages.docid: 28819
negative_passages.text: A union of two subspaces not equal to the vector space.
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?