Maximal resolvability of infinite products of non-singleton spaces

Determine whether every infinite product ∏_{i∈I} X_i of topological spaces, where I is an infinite index set and each X_i has at least two points, is maximally resolvable; equivalently, ascertain whether ∏_{i∈I} X_i can always be partitioned into Δ(∏_{i∈I} X_i) many dense subsets, where Δ denotes the dispersion character.

Background

Elkin (1969) established that the infinite product of non-singleton topological spaces is c-resolvable, guaranteeing the existence of continuum many dense subsets in such products. This provides a baseline level of resolvability for infinite products without additional separation axioms.

The open question concerns whether this lower bound can always be improved to maximal resolvability, i.e., achieving as many disjoint dense subsets as the dispersion character of the product allows. This problem sits at the intersection of product topology and resolvability theory, and an affirmative or negative resolution would refine our understanding of the structure of dense partitions in large products.