2 problems

Pseudo-solenoid projective-homogeneity conjecture. For every $\epsilon>0$, there exists a homeomorphism $\varphi$ of $C$ onto itself such that, for every $x\in C$,

Pseudo-circle projective-homogeneity conjecture. For every $\epsilon>0$, there exists a local homeomorphism $\varphi$ of $C$ onto itself such that, for every $x\in C$,