$\mathcal{S}$, smallest $\sigma$-algebra on $\mathbb{R}$ containing $\{(r,r+1):r\in\mathbb{Q}\}$, is the set of Borel subsets of $\mathbb{R}$
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
64118
Number of elements in a finite $\sigma$-algebra
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
83830
Sigma algebra generated by the set of all singletons
104234
What is the Hausdorff dimension of the set of irrationals on $\mathbb R^1$
104308
Proving a set is a Sigma Algebra
134310
Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
29637
$\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$
138768
Showing that the family of Borel sets is countably generated
62317
Generating set of countable, co-countable sigma algebra on $\mathbb{R}$
147486
Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?
14861
If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
80945
Borel subalgebras contain solvable radical