3 problems

Weaker nonexistence conjecture. There is no Borel morphism from $\bold R$ to $\bold R_3$.

Nonexistence conjecture. There is no Borel morphism from the old product of two copies of $\bold R$ to $\bold R_3$.

Let $\mathbb{M}$ be a strongly regular sequence. Define $\widetilde{S}_{\mathbb{M}}$ as the set of positive opening parameters for which the formal asymptotic Borel map is surjecti…