Is complement of open dense set measure zero in $\mathbb{R}^n$
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
131037
Is every compact subset of $\Bbb{R}$ the support of some Borel measure?
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
70264
Prove that the inverse image of an open set is open
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
80559
In $C[0,1]$ prove that the subset of Lipschitz functions is dense
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
17764
What's the relationship between Borel set and set whose boundary is measure zero?
15645
Is convex open set in $\mathbb{R}^n$ is regular?
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
51260
Sum of sets of measure zero
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
74720
Is every set of measure zero countable?
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure