Preservation of strong countable dimensionality under Cp‑homeomorphisms for NY compacta

Ascertain whether strong countable dimensionality is preserved under homeomorphisms of Cp‑spaces within the class of NY compact spaces: given NY compact spaces K and L with Cp(K) homeomorphic to Cp(L) and K strongly countable‑dimensional, determine whether L must also be strongly countable‑dimensional.

Background

Building on Theorem 5.6, the authors show NY compactness is a Cp‑homeomorphism invariant. For the w‑Corson class, which coincides with Corson compactness plus strong countable dimensionality, the authors explain that resolving Cp‑invariance reduces to whether strong countable dimensionality is preserved under Cp‑homeomorphisms in the NY class.

A positive answer would imply Cp‑homeomorphism invariance of the w‑Corson property, addressing the preceding unresolved question.