NY‑Valdivia status of continuous images of A(ω1)^ω

Determine whether every continuous image of the countable product A(ω1)^ω, where A(ω1) is the one‑point compactification of a discrete space of cardinality ω1, is an NY‑Valdivia compact space (i.e., admits an embedding into a product of Hilbert cubes ∏ Q_y such that the σ‑product σ(∏ Q_y) is dense in the image).

Background

The paper shows that uniform Eberlein compact spaces need not be NY‑Valdivia by exhibiting K = AD(A(ω1)^ω) as a counterexample. Since every uniform Eberlein compact space is a continuous image of a closed subspace of A(κ)^ω, this naturally leads to asking about the NY‑Valdivia status of continuous images specifically of A(ω1)^ω.

The question focuses on whether the NY‑Valdivia property is preserved under taking continuous images of the canonical product built from the one‑point compactification of a discrete uncountable space, a theme connected to polyadic spaces and their invariants.