A subset of $\mathbb{R}$ that neither is an $F_\sigma$ set nor a $G_\delta$ set
47937
Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
132382
Showing a set is nowhere dense in $C([0,1])$
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
42084
Set of points of continuity are $G_{\delta}$
89749
Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
100919
Examples of non-measurable sets in $\mathbb{R}$
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
136795
A non-measurable set of given outer measure
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
154621
A set with a finite integral of measure zero?
92309
The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$