On the seminormal functors with invariant extension to the Tych category

Using methods of Chigogidze, we can extense a seminormal functor acting in the category Comp to the category Tych. Researching the properties of this extension, we introduce the notion of a functor having an invariant extension to the category Tych. Let F be seminormal functor acting in the category Comp and X be Tychonoff space. By p (x) we denote the subspace of F(fiX) consisting of all points | such that supp X С X. Let bX be a compactification of X. Put F b (X) = { Є F(bX): supp X С X}. For the natural mapping f : fiX ^ bX consider the mapping F(f) | F (X : F p (X) ^ F b (X). We say that the functor F has an invariant extension to the category Tych if the mapping F(f) | F ( is a homeomorphism for any Tychonoff space X and its arbitrary compac- Fp( X) tification bX. We obtained the criterion of the invariant extension for a finite degree seminormal functor. We prove that any seminormal functor F with the degree spectrum spF = {1; n} hasn’t got an invariant extension for n > 4. For n = 3 there are the examples of the functors Я and џ with the degree spectrum spA 3 = sp џ == {1 ;3 } such that Я has an invariant extension, and џ has not.