Prove $d$ and $d'=\frac{d}{1+d}$ are equivalent metrics
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
132641
Proving that Euclidean Space is a complete metric space
157742
Prove that $U(n)$ is a manifold
98010
Constructing a metric on a Lie Group
150011
Proof completeness of $(X,d)$ given $d$ is French railway metric
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
8711
Problems in the relation $a=v\frac{\mathrm{d}v}{\mathrm{d}x}$
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
38127
Equivalence between Kähler condition and $\partial_kg_{i\bar j} = \partial_ ig_{k\bar j}$
56143
Proof of a basic $AC_\omega$ equivalence
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
78471
Closure of $\{\frac{1}{n}\}:=M$