$C^1[0,1]$ is not complete with respect to sup norm
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
86284
A typical $L^p$ function does not have a well-defined trace on the boundary
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
92774
Prove that a linear subspace of $C([0,1])$ is closed
33485
norm of integral operator in $C([0,1])$
108740
$C^1[a,b]$ is closed in $C[a,b]$
128558
Inequality between $\ell^p$-norms
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
121198
$W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
86717
Completeness of $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle$
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
121223
How to prove that the centering inequality for the sub-gaussian norm does not hold