Metric of the real numbers for which it is not complete
137881
A not complete metric space?
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
20135
Measure of  reals in $[0,1]$ which don't have $4$ in decimal expansion
23845
How to prove the continuity of the metric function?
27517
Isometry in compact metric spaces
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
93606
Showing that $C[0,1]$ is not complete
49374
Closure of a subset in a metric space
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
130149
Computablility of a real number
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
76434
What is the measure of the set of numbers in $[0,1]$ whose decimal expansions do not contain $5$?
111064
Example of a bounded lattice that is NOT complete
41675
Metric is continuous, on the right track?
52104
A pseudometric on the space of the measurable functions is complete
111119
Distance between any two points in a compact 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 $d(x,A)=d(x,a_0)$