query: If $A$ is bounded then so is $A\cdot A$?
positive_passages.docid: 144372
positive_passages.text: How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
negative_passages.docid: 135157
negative_passages.text: Totally bounded, complete $\implies$ compact
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 28685
negative_passages.text: If every linear operator on $X$ is bounded then is $\dim X<\infty$?
negative_passages.docid: 143695
negative_passages.text: Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
negative_passages.docid: 104914
negative_passages.text: Abount linear functional: If $T(B)$ is bounded, is $T$ bounded?
negative_passages.docid: 30330
negative_passages.text: How can I prove that this function is bounded using the given 2 hints?
negative_passages.docid: 103061
negative_passages.text: Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
negative_passages.docid: 17165
negative_passages.text: Is total boundedness a topological property?
negative_passages.docid: 16550
negative_passages.text: Is $ d(X) \le s(X)? $
negative_passages.docid: 121079
negative_passages.text: lemma: Cauchy sequences are bounded.
negative_passages.docid: 29849
negative_passages.text: How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
negative_passages.docid: 20571
negative_passages.text: In a monoid, does $x \cdot y=e$ imply $y \cdot x=e$?
negative_passages.docid: 6128
negative_passages.text: If $a \cdot a = 1$ then $a = 1$ or $a = -1$
negative_passages.docid: 136789
negative_passages.text: How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
negative_passages.docid: 28678
negative_passages.text: Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?
negative_passages.docid: 91352
negative_passages.text: If $\Re(f)$ is bounded then f is constant.