How to prove that the intersection of $L^1(\mathbb{R})$ and $L^2(\mathbb{R})$ is dense in $L^2(\mathbb{R})$
67244
Why is $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ dense in $ L^2(\mathbb{R}^n)$?
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
84189
Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
88523
Show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N} \} $ is dense in $\mathbb {R}$
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
108619
Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
68153
How to show that $L^p$ spaces are nested?
47975
Closed cone in the euclidean space $\mathbb{R}^n$
115625
Intersection of two open dense sets is dense
69166
Cardinality of $\mathbb{R}$ and $\mathbb{R}^2$
30568
Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$
6523
Prove that the space has a countable dense subset
48783
Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
66953
How to prove Laplace transform is bounded on $L^2(\mathbb{R}_+)$?
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$