On Tightness-Type Properties of the Space of Semiadditive Functionals of Finite Support

Abstract

We investigate tightness-type properties, in particular tightness and minitightness, of the space OS_n(X) of semiadditive functionals with finite support on a compact space X. We also work with strictly τ -continuous mappings in the sense of A.V. Arkhangelskii and show that the functor OS_n admits a natural extension to the category T ych(τ ) of Tychonoff spaces and strictly τ -continuous maps. For infinite compact spaces X we prove that the functor OS_n preserves both tightness and minitightness.