AlexMennen comments on Formal Open Problem in Decision Theory

[AlexMennen]

I haven’t checked that argument carefully, but that sounds like it should give you $X^{\prime }$ with a continuous bijection $\varphi :X^{\prime }\to [0,1{]}^{X^{\prime }}$, which might not necessarily be a homeomorphism.

[Stuart_Armstrong]

Yes, you’re right.