$\sigma$-algebra that is countable, but not finite
43894
If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
134983
Borel sigma algebra not containing all subsets of $\mathbb{R}$?
33207
Bases having countable subfamilies which are bases in second countable space
55717
cardinality of the Borel $\sigma$-algebra of a second countable space
48174
Are countable topological spaces second-countable?
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
47937
Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$
10702
Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
84936
The set of all finite sequences of members of a countable set is also countable
78256
Finite additivity in outer measure
34298
sequentially continuous on a non first-countable
32774
Finite Cartesian Product of Countable sets is countable?
19996
Example where union of increasing sigma algebras is not a sigma algebra
44974
Infinite set and countable subsets
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
92309
The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$