query: Does a Bounded linear transformation from a Banach space to Real numbers map a bounded closed set to a closed set?
positive_passages.docid: 17262
positive_passages.text: Bounded operator that does not attain its norm
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: 125277
negative_passages.text: Image of the tensor product of strict maps of Banach spaces
negative_passages.docid: 52388
negative_passages.text: The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
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: 42494
negative_passages.text: The boundary is a closed set
negative_passages.docid: 11586
negative_passages.text: Sequences of Real Numbers in a closed bounded interval
negative_passages.docid: 71001
negative_passages.text: Do continuous linear functions between Banach spaces extend?
negative_passages.docid: 66691
negative_passages.text: Real function continuous on closed interval implies it is bounded - over-simple proof??
negative_passages.docid: 32534
negative_passages.text: Prove that a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$.
negative_passages.docid: 144400
negative_passages.text: Are compact subsets of metric spaces closed and bounded?
negative_passages.docid: 14840
negative_passages.text: $c_0$ is a closed subspace of $l^{\infty}$
negative_passages.docid: 103397
negative_passages.text: Homeomorphisms between infinite-dimensional Banach spaces and their spheres
negative_passages.docid: 83054
negative_passages.text: Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
negative_passages.docid: 78344
negative_passages.text: Nonconstant linear functional on a topological vector space is an open mapping
negative_passages.docid: 92774
negative_passages.text: Prove that a linear subspace of $C([0,1])$ is closed
negative_passages.docid: 97148
negative_passages.text: Does bounded variation imply boundedness