Cp‑homeomorphism invariance of the w‑Corson class

Establish whether the class of w‑Corson compact spaces is invariant under homeomorphisms of Cp(X): specifically, determine whether for compact spaces K and L with Cp(K) homeomorphic to Cp(L) and K w‑Corson, it follows that L is w‑Corson.

Background

The authors prove that NY compactness is invariant under homeomorphisms of Cp‑spaces (Theorem 5.6). They then note that the analogous statement for the w‑Corson class is unresolved.

Using known characterizations (including [13, Corollary 5.1]) they indicate the issue reduces to strong countable dimensionality considerations as formulated in Question 5.7.