How to show that $\Bbb R^m$ is not diffeomorphic to $\Bbb R^n$ when $n \neq m$
63845
Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
113915
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
54875
How to prove polynomials with degree $n$ does not form a vector space?
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
79285
Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
158127
Quotient space of $\Bbb C^n$ obtained by action of $S_n$
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$