Some generalization of the Arkhangel'skiĭ–Kombarov theorem for seminormal functors

We introduce the notion of variative seminormal functor $\mathscr F$ and prove that, for each of these functors and every compact space $X$, the normality of the space $\mathscr F(X)\setminus X$ is countable. Thus, we obtain a generalization of the Arkhangel'skiĭ–Kombarov theorem of 1990 on the countability of the character of a compact space which is normal outside the diagonal. Under the assumption of Jensen's principle, we prove that the above assertion fails for finite nonvariative functors.