On the functor of semiadditive \(\tau\)-smooth functionals. (English) Zbl 1375.54010
Summary: We investigate categorical and topological properties of the functor \(O S_\tau\) 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 \(O S_\tau\) is a normal functor in the category \(Tych\) of Tychonoff spaces.
MSC:
| 54B30 | Categorical methods in general topology |
| 18A22 | Special properties of functors (faithful, full, etc.) |
| 46A63 | Topological invariants ((DN), (\(\Omega\)), etc.) for locally convex spaces |
| 46E27 | Spaces of measures |
| 54A25 | Cardinality properties (cardinal functions and inequalities, discrete subsets) |
| 54C35 | Function spaces in general topology |
| 18B20 | Categories of machines, automata |
| 18A05 | Definitions and generalizations in theory of categories |
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