query: Metric mapping to sets other than $\Bbb{R}$
positive_passages.docid: 142414
positive_passages.text: Generalization of metric spaces?
negative_passages.docid: 112303
negative_passages.text: Distances between closed sets on metric spaces
negative_passages.docid: 30597
negative_passages.text: Morphism that is not a mapping
negative_passages.docid: 106698
negative_passages.text: $\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
negative_passages.docid: 35156
negative_passages.text: Constructing a choice function in a complete & separable metric space
negative_passages.docid: 52014
negative_passages.text: Showing $(C[0,1], d_1)$ is not a complete metric space
negative_passages.docid: 90110
negative_passages.text: Hyperbolic metric geodesically complete
negative_passages.docid: 33427
negative_passages.text: Why is Euclidean distance not a good metric in high dimensions?
negative_passages.docid: 124688
negative_passages.text: Question about a metric on $\mathbb{R}^2$
negative_passages.docid: 152196
negative_passages.text: About inner products, norms and metrics
negative_passages.docid: 3537
negative_passages.text: Show the Euclidean metric and maximum metric are strongly equivalent.
negative_passages.docid: 99816
negative_passages.text: Existence of Topologically Transitive Maps on nice Metric Spaces
negative_passages.docid: 6415
negative_passages.text: Distance function is continuous in topology induced by the metric
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: 114061
negative_passages.text: Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
negative_passages.docid: 126759
negative_passages.text: Unbounded continuous function on non-compact metric space
negative_passages.docid: 70106
negative_passages.text: diameter on a compact metric space