query: Can any metric on $\Bbb R^n$ be bounded above and below for any other metric?
positive_passages.docid: 18195
positive_passages.text: Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces
negative_passages.docid: 45939
negative_passages.text: For which $n≥2$ does there exist $\sigma\in A_n$ with $|\sigma| > n$
negative_passages.docid: 69777
negative_passages.text: Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
negative_passages.docid: 49563
negative_passages.text: Cauchy nets in a metric space
negative_passages.docid: 53812
negative_passages.text: Metric is continuous function
negative_passages.docid: 73254
negative_passages.text: spectral radius in normed space is subadditive.
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 27517
negative_passages.text: Isometry in compact metric spaces
negative_passages.docid: 137881
negative_passages.text: A not complete metric space?
negative_passages.docid: 60868
negative_passages.text: Interplay of Hausdorff metric and Lebesgue measure
negative_passages.docid: 1760
negative_passages.text: Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
negative_passages.docid: 128894
negative_passages.text: About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
negative_passages.docid: 44955
negative_passages.text: Can $\mathbb CP^n$ be the boundary of a compact manifold?
negative_passages.docid: 36566
negative_passages.text: Equivalence classes and metric spaces
negative_passages.docid: 50677
negative_passages.text: Is this metric space incomplete?
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$