Некоторые свойства полунормальных функторов

In the paper the normality of the space of maximal 3-linked systems is studied as well as the problem of building a maximal linked system with given support. The answer to the question, whether it is possible to define a superextension's subfunctor in the same way as continious exponent functor with the use of support's concept, is given. It is also proved, that for seminormal functors, preserving one-to-one points, $sp\mathcal{F} = \{1, k,\dots \}$, where $k\le 3$.