Prove that $C^1[0,1]$ is not complete with norms
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
93606
Showing that $C[0,1]$ is not complete
127248
Norm and unit sphere
140692
Existence of a complete metric on $(0,1)$
49087
Show that a norm on an inner product space satisfies parallelogram law.
63608
Cauchy sequence in a normed space
118564
Dual cone of a $L^1$ norm cone?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
142901
"The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
157455
Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
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 $\mathbb R^1$
74764
Dimension for a closed subspace of $C[0,1]$.
128558
Inequality between $\ell^p$-norms
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
33485
norm of integral operator in $C([0,1])$