Tool for contradiction proof that $S^2 \not\approx \mathbb{R}^2$
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
79285
Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
5250
Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
27775
Proving a function is not a contraction
88051
$\mathbb R = X^2$ as a Cartesian product
118577
Fallacious proof involving trigonometry
104548
Geometric proof for irrationality of $\pi$
86537
Prove that an open interval and a closed interval are not homeomorphic
151637
How do we prove that this set is not manifold?
119139
Show that antipodal points remain antipodal under any isometry of $S^2$
25397
Prove $R \times R$ is NOT an integral domain
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
14447
Direct proof that $\pi$ is not constructible
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?