Prove a given distance function is in fact a metric: $ d(f,g) = \sup\limits_{x\in X}|f(x)-g(x)| $
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
18040
Show that a compact metric space is bounded
27652
metric on the Euclidean Group
134601
whether they are complete metric space
104044
Prove continuous functions $f$ and $g$ are equal
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
133504
Suppose $X$ is a metric space and $S \subseteq X.$ Then, $S^o=\{x \in X~|~dist(x,S^c)>0\}$.
140124
The distance function on a metric space
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
35573
A closed ball in a metric space is a closed set
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
142414
Generalization of metric spaces?
23203
Euclidean distance proof
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).
46834
show that a distance function is continuous
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?