Any open set $G\subset\mathbb{R}$ has the form $G=\sqcup_i (a_i,b_i)$.
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
16654
Unions and Intersections of Open Sets are Open
27899
Can we prove the existence of $A\cup B$ without the union axiom?
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
112523
Does $\sqsubset$ have any special meaning?
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
110217
$GL(n,K)$ is open in $M(n,K)$
99236
Interior of closure of an open set
152825
what are all the open subgroups of $(\mathbb{R},+)$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
41611
Open and closed set in n by n matrices space.
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.