triangle inequality of metric d(x,y)
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
104413
Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
129161
The minimum perimeter and maximum height of a triangle under constraints
128786
How to use triangle inequality to establish Reverse triangle inequality
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
142414
Generalization of metric spaces?
94218
Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.
107321
How to show convexity of a ball in metric space?
126944
Metric spaces problem
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
86305
A secant inequality for convex functions
132641
Proving that Euclidean Space is a complete metric space
11983
Proof of Clarkson's Inequality
72033
Is this proof sufficient to show that a concave function of a metric is also a metric?
27517
Isometry in compact metric spaces