2 problems

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Nonexistence of a Borel morphism from the binary splitting relation to the three-piece splitting relation
Weaker nonexistence conjecture. There is no Borel morphism from $\bold R$ to $\bold R_3$ .
Conjectureopenborel-maps cardinal-characteristics relational-systemsarXiv posted 2 days ago
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Nonexistence of a Borel morphism from the old product to the three-piece splitting relation
Nonexistence conjecture. There is no Borel morphism from the old product of two copies of $\bold R$ to $\bold R_3$ .
Conjectureopenborel-maps cardinal-characteristics relational-systemsarXiv posted 2 days ago

Nonexistence of a Borel morphism from the binary splitting relation to the three-piece splitting relation