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 X 2 ∖ { ( p , p ) } implies the countability of character of X at the point p.