Proving that the functional $T_x : (C[0,1], \| \cdot \|_1) \rightarrow \mathbb{R}$ is not bounded, where $T_x(f) = f(x)$ and $x \in [0,1]$.
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
68724
$||T-I|| < 1$ implies that $T$ is invertible.
142232
Functional Analysis. Continuous extensions of linear functionals.
135449
Prove: $\frac1x$ is not a uniformly continuous function
61640
Prove c exists for f:[0,1] -> R
134382
Proving bounded first derivative
84318
A problem with the functional $F(\chi) = \int_{\mathbb{R}}(\chi'^2+\chi^2(1-\chi)^2)dx$.
152590
At most finitely many (Hamel) coordinate functionals are continuous - different proof
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
113122
Prove that a continuous real function with finite limits is bounded
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
33485
norm of integral operator in $C([0,1])$
28888
The functional $I[w] = \int_U \frac{1}{2} |Dw|^2 - fw \, dx$ is weakly lower semicontinuous
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$