Is $\mathbb{R}\setminus\mathbb{Q}$ separable?
30796
Is the set of irrationals separable as a subspace of the real line?
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
157565
Is every dense subspace of a separable space separable?
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
125894
Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
96354
Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
105791
Does separability imply the Lindelöf property?
37953
Primary Decomposition of $\mathbb{R^n}$ under T
88301
What are all of the connected subsets of $\mathbb{Q}$?
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?