ИСТИНА

Functors $U^\epsilon$, $\epsilon=\beta, R,\tau$ of the unit ball of alternating Borel measure are investigated. It is shown that these functors satisfy only three of the seven properties of normality, inherent in functors probability measure. Namely, these functors are almost continuous, preserve maps with dense images and intersections of closed subsets normal space. In addition, for an infinite discrete space $X$ space $U^\epsilon(X)$ does not satisfy the first axiom of countability and does not even spaces are Frechet-Uryson. It follows that the $U^\epsilon:{\bf Tych}\to{\bf Tych}$ functors do not preserve topological embeddings, the weight of topological spaces and their metrizability. Also, these functors do not retain perfect mappings (even spaces with counting base). It is worth noting that in the category ${\bf Comp}$ compact spaces functor $U=U^\beta=U^R=U^\tau$ has all the properties of a normal functor except properties for saving an empty set, point, and preimages.