К вопросу о наследственной нормальности пространств вида $\mathcal{F}(x)$

Ivanov and Kashuba [1] constructed an example assuming the Continuum Hypothesis. There exists a nonmetrizable compact space $X$, such that the following conditions hold: 1) for any natural number $n$ the compact space $X^{n}$ is hereditarily separable; 2) for any natural number $n$ the space $X^{n}\setminus \Delta_{n}$ is hereditarily normal; 3) for any functor $\mathcal{F}$ preserving weight and one-to-one points the space $\mathcal{F}_{k}(X)$ is hereditarily normal ($k$ is the second element of the degree spectrum $sp(\mathcal{F}))$.