Prove: $d(x,y)=\frac{1}{\min\{i\in \mathbb{N}:x_i\neq y_i\}}$ is a metric
135315
Proving whether a function on the set of real sequences is a metric
107321
How to show convexity of a ball in metric space?
152057
Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
27517
Isometry in compact metric spaces
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
11094
How to prove that the French railways metric is a metric
65827
When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
49721
Prove the empty set is closed for a metric space (X,d).
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
27652
metric on the Euclidean Group
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
35573
A closed ball in a metric space is a closed set
127034
Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$
62479
A isometric map in metric space is surjective?
69528
Metrizability of quotient spaces of metric spaces
144353
A closed ball in a metric space is closed