Show this induced metric is a metric
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
60868
Interplay of Hausdorff metric and Lebesgue measure
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
83159
Defining a metric space
152196
About inner products, norms and metrics
124179
Proof that every metric space is normal
79861
Induced metric on a null hypersurface
23845
How to prove the continuity of the metric function?
92340
How many metrics are there on a set up to topological equivalence?
94438
Show that the countable product of metric spaces is metrizable
134601
whether they are complete metric space
78108
Do these define metrics on $\mathbb{R}$?
39763
Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
55016
Prove that if ($d(x,y)=0$ iff $x=y$) and if $d(x,z)\leq d(x,y)+d(z,y)$ then $d$ is a metric
11094
How to prove that the French railways metric is a metric
107321
How to show convexity of a ball in metric space?