Showing that the derivative function is not continuous w.r.t. the sup norm
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
76140
The supremum norm is submultiplicative
42302
Use of Holder inequality in gradient estimate for harmonic function.
124499
Where is the error in my proof that all derivatives are continuous?
9159
$L^p$-norm of a non-negative measurable function
12523
Supremum of a Continuous Function is Continuous
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
158567
A uniform continuous function which is not Hölder continuous
127538
Show $f(x)=x\ln x$ is not uniformly continuous
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
74145
How to prove $x^{n}$ is not uniformly continuous
119479
Derivative with respect to a 2-norm
12408
Prove that a function whose derivative is bounded is uniformly continuous.
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.
38761
Is the $ L^{p}$$[0,1]$ norm continuous in p?
144382
Proving $\lVert x \rVert_3$ is smaller than euclidean norm