The space $C^1[a,b]$ with respect to the norm $\int ^a _b |f| +\int ^a _b |f'|$ is not complete
107984
Is $C^1[a,b]$ with the norm $\left \| f \right \|_1=(\int_{a}^{b}\left | f(t) \right |dt)+(\int_{a}^{b}\left | f´(t) \right |dt)$ a complete space?
107389
Show that the vector space of real functions is not finitely spanned
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 $\mathbb R^1$
43897
An integral inequality (Rudin $L^p$-spaces 3.12)
77716
Not every metric is induced from a norm
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
63608
Cauchy sequence in a normed space
113696
Showing that the unit ball in $(C^\alpha[a, b], \|\cdot\|_\alpha)$ is compact in $(C[a, b], \|\cdot\|_\infty)$
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
150287
Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
93606
Showing that $C[0,1]$ is not complete
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
10907
Necessity of completeness of the inner product space in Riesz representation theorem
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
98756
Unit ball in $C[0,1]$ not sequentially compact
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?