Show that this is a metric?
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
65840
Norm induced by metric
98010
Constructing a metric on a Lie Group
90110
Hyperbolic metric geodesically complete
42638
Showing that a function $f$ has a unique fixed point in a metric space.
65334
Show that a certain set is measurable
146215
Metric on a Quotient of the Riemann Sphere
3751
Proving a distance between molecules defines a metric space.
46834
show that a distance function is continuous
113688
Is Topological Space a Metric Space?
27517
Isometry in compact metric spaces
80274
What is the "topology induced by a metric"?
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
92340
How many metrics are there on a set up to topological equivalence?
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
132528
Are metrics that determine the same topology, equivalent?
146967
Understanding equivalent metric spaces