On completness of $\mathbb{R}$
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
140868
Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
24050
Characterization of the Closure of a Set
131664
Why is any Lebesgue-Stieltjes measure on $(\mathbb{R},\mathcal{B}_\mathbb{R})$ not complete?
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
56728
Question about limit points of a Subset of $\mathbb{R}$
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
81423
Completeness and Topological Equivalence
134844
Summablity and countability
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
74498
Smallest dense subset of $\mathbb{R}$
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
45405
An elementary way to show any bounded subset of $\Bbb{R}^k$ is totally bounded