On the functor of semiadditive τ-smooth functionals

In the work we investigate categorical and topological properties of the functor OSτ of semiadditive τ-smooth functionals in the category Tych of Tychonoff spaces and their continuous mappings, which extends the functor OS of semiadditive functionals in the category Comp of compact spaces and their continuous mappings. It is proved that the functor OSτ is a normal functor in the category Tych of Tychonoff spaces.