Open set in $\mathbb{R}$ as countable union of open intervals and which version of Choice
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
75829
Dimension of open subsets of $R^n$
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
139247
Real Analysis - Prove a set is countable
121626
Every open cover of the real numbers has a countable subcover (Lindelöf's lemma)
24050
Characterization of the Closure of a Set
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
136106
Is every open subset of $ \mathbb{R} $ uncountable?
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
107160
Open Set and Measure Theory
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 $\mathbb R^1$
15645
Is convex open set in $\mathbb{R}^n$ is regular?
15480
Open set in a metric space is union of closed sets
135454
An open interval is an open set?
105445
Are the rationals a closed or open set in $\mathbb{R}$?