Doesn't the standard proof of "Sierpinski's Theorem" work in ZF?
Where is choice used in the proofs below? Could it be easily eliminated if the sets $X_i$ were assumed to be singletons?
"Continuum" below means compact connected Hausdorff.
Doesn't the standard proof of "Sierpinski's Theorem" work in ZF?
Where is choice used in the proofs below? Could it be easily eliminated if the sets $X_i$ were assumed to be singletons?
"Continuum" below means compact connected Hausdorff.