is $\sigma$-algebra $\mathcal{F}_1 =$ {$X \subset \mathbb{R}: X \textrm{ or } \mathbb{R} \setminus X \textrm{ is countable}$ } countably generated?
62317
Generating set of countable, co-countable sigma algebra on $\mathbb{R}$
16892
Reference request: product Borel $\sigma$-algebra of non-separable metric spaces
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
136094
$G_\delta$ singletons in compact Hausdorff and first countability
35140
Existence of minimal $\sigma$-algebra and transfinite induction
84460
If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
81873
Is $(X,\mathcal T)$ necessarily an indiscrete space?
139622
Generator of rational functions unchanged under $\sigma(X) = X + 1$
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
110832
$F_\sigma$-subsets in a normal space can be separated
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
134983
Borel sigma algebra not containing all subsets of $\mathbb{R}$?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
55717
cardinality of the Borel $\sigma$-algebra of a second countable space
74720
Is every set of measure zero countable?