Prove that $\mathbb{R}^{n}_{1}$ is not isometric to $\mathbb{R}^{n}_{\infty}$ for $n>2$.
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
120623
Unit sphere in $\mathbb{R}^\infty$ is contractible?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
156727
A step in the proof of Characterization of $W^{1,\infty}$
105772
Definition of $\mathbb{R}^\infty$
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
7815
Prove that $\lim_{n\to\infty}a_n^2=a^2$ when ${a_n}$ is a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$
6491
Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
99675
A closed ball in $l^{\infty}$ is not compact
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded