An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal

Under Jensen's axiom, a compact space $X$ of uncountable character such that the space $\exp_n(X)\setminus X$ is normal for each $n$ is constructed. Thereby, it is proved that the Arkhangelskii–Kombarov theorem on the countability of the character of a compact space whose square is normal outside the diagonal cannot be “naïvely” carried over to normal functors of finite degree.