Let $(C[-1,1],\|.\|_2)$ prove this space isn't a Banach space.
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
156457
Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
47231
The space $C^0([0;1],\mathbb{R})$ of all continuous, real-valued functions on $[0,1]$ is not reflexive.
73248
Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
80618
Surjective bounded operator in Banach spaces without bounded right-inverse
33642
Finite dimensional subspace of $C([0,1])$
131890
Totally disconnected space that is not $T_2$
62428
How to prove this inequality in Banach space?
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
41620
The dual space of $c$ is $\ell^1$
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$