The compact space such that the space $\lambda^3(X)$ of maximal $3$-linked systems is not normal is constructed. It is proved that for any product of infinite separable spaces there exists a maximal linked system with the support equal to the product space. It is proved that a set of maximal $3$-linked systems with continious supports is everywhere dense in the superextension $\lambda(X)$ if $X$ is connected and separable. The properties of seminormal functors preserving one-to-one points are discussed.