query: prove that the set A/B is compact
positive_passages.docid: 147237
positive_passages.text: If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.
negative_passages.docid: 22854
negative_passages.text: Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
negative_passages.docid: 80827
negative_passages.text: Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
negative_passages.docid: 144360
negative_passages.text: For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
negative_passages.docid: 148994
negative_passages.text: $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
negative_passages.docid: 3708
negative_passages.text: How can I prove that compact subset iff sequentially compact in second countable topological spaces?
negative_passages.docid: 43376
negative_passages.text: If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 18040
negative_passages.text: Show that a compact metric space is bounded
negative_passages.docid: 58948
negative_passages.text: If $A$ is compact, is then $f(A)$ compact?
negative_passages.docid: 8015
negative_passages.text: Compact set plus a closed set is a closed set
negative_passages.docid: 11817
negative_passages.text: Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$
negative_passages.docid: 118239
negative_passages.text: If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
negative_passages.docid: 48783
negative_passages.text: Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
negative_passages.docid: 90590
negative_passages.text: Prove that the following set is dense
negative_passages.docid: 83311
negative_passages.text: Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
negative_passages.docid: 47810
negative_passages.text: $C(X)$ is separable when $X$ is compact?