3 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 $x\in C$,

Irwin–Solecki's conjecture. It should be possible, after appropriate adjustments of definitions, to develop a theory for pseudo-solenoids similar to the approximate projective-homo…