Is there a set $E$ such that for every open interval $I$, $0<m(I\cap E)<m(I)$?
3023
Construction of a Borel set with positive but not full measure in each interval
157753
Show that any set in a metric space can be written as the intersection of open sets
73130
A simple question about open set
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
137099
Lebesgue measure of the set of zeroes of Brownian motion
24050
Characterization of the Closure of a Set
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
92571
Sets with no asymptotical density over $\mathbb N$
78786
Why does an open interval NOT have measure zero?
91736
Explicit homeomorphism between open and closed rational intervals?
152976
Real Analysis: open and closed sets
148638
Write $(0,1)$ as a countable union of disjoint open intervals
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
128987
A collection of pairwise disjoint open intervals must be countable