Does there exist a metric under which $\mathbb{R}$ is incomplete?
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
28683
Sum of two closed sets in $\mathbb R$ is closed?
118617
Completeness and Incompleteness
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
47975
Closed cone in the euclidean space $\mathbb{R}^n$
83159
Defining a metric space
33427
Why is Euclidean distance not a good metric in high dimensions?
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
90110
Hyperbolic metric geodesically complete
74607
Variation of the metric with respect to the metric
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
43248
Closure of a Ball is Contained in Closed Ball (usual metric)
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
77867
Existence of a Riemannian metric inducing a given distance.
100919
Examples of non-measurable sets in $\mathbb{R}$