Kopczyński-type union closure remains open beyond ω-regular objectives

Ascertain whether the union of two prefix-independent positional objectives is positional in full generality, i.e., for arbitrary (not necessarily ω-regular) objectives over infinite games.

Background

While the paper settles the union closure (in a stronger form) for ω-regular objectives when one operand is prefix-independent, the authors note that the general version for arbitrary objectives remains unresolved.