query: A necessary and sufficient condition for $B \subset \ell^1$ to be compact
positive_passages.docid: 18596
positive_passages.text: A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
negative_passages.docid: 113790
negative_passages.text: $\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 92497
negative_passages.text: Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
negative_passages.docid: 127173
negative_passages.text: Closed subset of compact set is compact
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
negative_passages.docid: 141642
negative_passages.text: Closure of a certain subset in a compact topological group
negative_passages.docid: 12467
negative_passages.text: Why does this proof work: Closed unit ball in $C_0$ is not compact
negative_passages.docid: 131037
negative_passages.text: Is every compact subset of $\Bbb{R}$ the support of some Borel measure?
negative_passages.docid: 8015
negative_passages.text: Compact set plus a closed set is a closed set
negative_passages.docid: 43376
negative_passages.text: If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
negative_passages.docid: 69497
negative_passages.text: Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
negative_passages.docid: 54957
negative_passages.text: The necessary and sufficient condition for a unit element in Euclidean Domain
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 14219
negative_passages.text: Is the intersection of a closed set and a compact set always compact?
negative_passages.docid: 47810
negative_passages.text: $C(X)$ is separable when $X$ is compact?
negative_passages.docid: 98756
negative_passages.text: Unit ball in $C[0,1]$ not sequentially compact