0
$\begingroup$

I have this problems

  1. Proof that the ball $B_1{(0,0)}$ can be embedded in Moore plane (Niemytzki plane)
  2. Proof that $({\mathbb R}^3; \textrm{usual topology})$ can be embedded in Moore plane (Niemytzki plane)
  3. Proof that $({\mathbb R}; \textrm{usual topology})$ can be embedded in Moore plane (Niemytzki plane)
    For the second I dont know if the function $h(x)=\left(x,\arctan(x)+ \frac{\pi}{2}\right)$ is right.

Thanks

1 Answers 1