On seminormal functors and compact spaces of uncountable character

We prove that for every seminormal functor F of finite degree n>1 and a compact space X of uncountable character at a point p∈X the space F(X)∖{p} is not normal. This generalizes a theorem of A.V. Arhangelʼskiĭ and A.P. Kombarov (1990) [1] asserting that for every compact space X the normality of the space X2∖{(p,p)} implies the countability of character of X at the point p.