$\frac{d}{1+d}$ is a metric
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
146967
Understanding equivalent metric spaces
107321
How to show convexity of a ball in metric space?
91000
Prove that $\frac{1}{a+1}0$
151984
Proving the existence of a metric space
72033
Is this proof sufficient to show that a concave function of a metric is also a metric?
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
155066
Dimension of the quotient space $\frac{C_{0}}{M}.$
50677
Is this metric space incomplete?
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
83159
Defining a metric space
15365
Proving that the triangle inequality holds for a metric on $\mathbb{C}$
140692
Existence of a complete metric on $(0,1)$
98660
(complex measures) $d\nu=d\lambda +f\,dm \Rightarrow d|\nu|=d|\lambda| +|f|\,dm$ and $f\in L^1(\nu)\Rightarrow f\in L^1(|\nu|)$