Show that there is a point $x$ on the surface such that $T(x) = T(-x)$. Hint: Represent surface of Mars as $\{x \in \mathbb{R}^{3} : \|x\| = 1 \}$
92802
Proof of Borsuk-Ulam Theorem .
154327
$A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
149801
prove that $TS = ST$
108837
How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
151958
How to show $f'(0)$ exist and is equal to $1$?
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
23414
Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
101374
Darboux Theorem Question
105852
How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
131881
Show that the roots of P' lie in the same half plane as the roots of P
109288
Prove that $x^3+y^3+z^3-3xyz=1$ defines a surface of revolution
30246
Find the equation of the tangent plane to the surface $x^{\frac{2}{3}}+y^{\frac{2}{3}}+z^{\frac{2}{3}}=2^{\frac{2}{3}}$ at $(x_0,y_0,z_0)$
67106
Projection on the hyperplane $H: \sum x_i=0$
15596
Identification of each tangent space $T_pV$ with $V$ itself?
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$