query: What is an example of infinite dimensional subspace that is not closed?
positive_passages.docid: 145668
positive_passages.text: Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 95635
negative_passages.text: $\ell^{\infty}(\mathbb N)$ is not a separable space
negative_passages.docid: 28819
negative_passages.text: A union of two subspaces not equal to the vector space.
negative_passages.docid: 141762
negative_passages.text: The direct sum of two closed subspace is closed? (Hilbert space)
negative_passages.docid: 115272
negative_passages.text: Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
negative_passages.docid: 82355
negative_passages.text: When is the image of a linear operator (between Banach spaces) closed?
negative_passages.docid: 129227
negative_passages.text: An example of neither open nor closed set
negative_passages.docid: 113498
negative_passages.text: Example of topological spaces where sequential continuity does not imply continuity
negative_passages.docid: 139988
negative_passages.text: Counter example for a result of intersection of subspaces
negative_passages.docid: 10034
negative_passages.text: Give an example of a non-separable subspace of a separable space
negative_passages.docid: 26329
negative_passages.text: Is there a shape with infinite area but finite perimeter?
negative_passages.docid: 145415
negative_passages.text: Examples of almost compact spaces.
negative_passages.docid: 64261
negative_passages.text: example of not surjective isometry on a bounded not closed set.
negative_passages.docid: 110726
negative_passages.text: Example of a non-gcd domain
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 11301
negative_passages.text: Union of two vector subspaces not a subspace?