Metric space $X=(0,1)$ with $d(x,y):= \vert \tan x-\tan y \vert$ complete or not?
50677
Is this metric space incomplete?
3751
Proving a distance between molecules defines a metric space.
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
137881
A not complete metric space?
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
49374
Closure of a subset in a metric space
154978
Some equivalent formulations of compactness of a metric space
127034
Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
146485
Prove that the product space is a metric space.
49503
Why does the natural quotient metric works in this case?
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
104413
Is the exponential of $-d$ a positive definite kernel for a general 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 $X=C[0,1]$
134601
whether they are complete metric space
113688
Is Topological Space a Metric Space?
124179
Proof that every metric space is normal