Proving $S^3$ and $\mathbb{R}^3$ are not homeomorphic
11762
Compactness of a Sphere
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
147310
How does one prove that the Klein bottle cannot be embedded in $R^3$?
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
139288
Formal proof that $e^x$ is not algebraic
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
39453
How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
25854
$\mathbb{R}^3$ \ $\mathbb{Q}^3$ is union of disjoint lines. The lines are not in an axis diretion.
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
151637
How do we prove that this set is not manifold?
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
14447
Direct proof that $\pi$ is not constructible
32765
$\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.