query: A metric on $\mathbb {P(N)}$.
positive_passages.docid: 17067
positive_passages.text: To prove that $(\mathbb{P(N)},d)$ is a metric space
negative_passages.docid: 92005
negative_passages.text: Existence of compact/complete metric on countable set
negative_passages.docid: 132641
negative_passages.text: Proving that Euclidean Space is a complete metric space
negative_passages.docid: 154076
negative_passages.text: How to show this property of $\mathbb{RP}^{n}$.
negative_passages.docid: 121359
negative_passages.text: Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
negative_passages.docid: 154978
negative_passages.text: Some equivalent formulations of compactness of a metric space
negative_passages.docid: 77867
negative_passages.text: Existence of a Riemannian metric inducing a given distance.
negative_passages.docid: 137881
negative_passages.text: A not complete metric space?
negative_passages.docid: 140692
negative_passages.text: Existence of a complete metric on $(0,1)$
negative_passages.docid: 9775
negative_passages.text: Metric on Cartesian Product
negative_passages.docid: 117716
negative_passages.text: Condition on function $f:\mathbb{R}\rightarrow \mathbb{R}$ so that $(a,b)\mapsto | f(a) - f(b)|$ generates a metric on $\mathbb{R}$
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 62479
negative_passages.text: A isometric map in metric space is surjective?
negative_passages.docid: 66550
negative_passages.text: Cardinality of separable metric spaces
negative_passages.docid: 112329
negative_passages.text: Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
negative_passages.docid: 142414
negative_passages.text: Generalization of metric spaces?
negative_passages.docid: 123039
negative_passages.text: If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.