In the work we investigate categorical and topological properties of the functor $OS_{\tau } $ of semiadditive $\tau $-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 $OS_{\tau } $ is significantly different from the functor $O_{\tau } $, as it preserves the preimages and nonempty intersections of closed subsets of Tychonoff spaces. One of the main results is that the functor $OS_{\tau } :Tych\to Tych$ is normal.