Are mT*-Baire spaces C(B)-spaces?

Determine whether every mT*-Baire space E is a C(B)-space, meaning that every nearly continuous mapping with closed graph from any Baire space F to E is continuous.

Background

The tandem Michael game (mT) defines mT*-Baire spaces, in which player α′ has a strong winning strategy. The paper proves that regular mT*-Baire spaces yield closed graph theorems in several settings and extend Pettis-type results.

However, whether the mT*-Baire property suffices to make a space a C(B)-space—i.e., to satisfy a closed graph theorem for all Baire source spaces—remains unresolved, with the authors expecting a negative answer.