Writing $\mathbb{R}$ as union of more than one disjoint open sets
2575
Showing that $\mathbb{R}$ is connected
95244
Prove that a finite union of closed sets is also closed
72468
Open and closed balls in $C[a,b]$
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
41611
Open and closed set in n by n matrices space.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
80156
Formatting the union of sets
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
18223
Prove that the union of two disjoint countable sets is countable
88981
Explicit Homeomorphism from $\mathbb{R}^2$ to open disk
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
24372
Infinite Set is Disjoint Union of Two Infinite Sets
130361
Basis for a topology with a countable number of sets
123897
Sum of two open sets is open?
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
70264
Prove that the inverse image of an open set is open