$C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
46326
The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
63516
$C^1[0,1]$ is not complete with respect to sup norm
63608
Cauchy sequence in a normed space
53850
Proof that every normed vector space is a topological vector space
109632
Show reflexive normed vector space is a Banach space
91173
Finite-dimensional subspace normed vector space is closed
127121
The identity cannot be a commutator in a Banach algebra?
64840
A Banach space that is not a Hilbert space
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
84264
the space of lipschitz function is complete with respect to some norm
82355
When is the image of a linear operator (between Banach spaces) closed?
4717
The union of linear subspaces is not necessarily a subspace
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..