Inclusion hyperspaces and capacities on Tychonoff spaces: functors and monads

The inclusion hyperspace functor, the capacity functor and monads for these functors have been extended from the category of compact Hausdorff spaces to the category of Tychonoff spaces. Properties of spaces and maps of inclusion hyperspaces and capacities (non-additive measures) on Tychonoff spaces are investigated.

💡 Research Summary

The paper extends two well‑studied constructions from the category of compact Hausdorff spaces to the broader category of Tychonoff spaces: the inclusion‑hyperspace functor G and the capacity (non‑additive measure) functor C. In the compact setting, an inclusion hyperspace is a family of closed subsets that is upward closed, and a capacity is a monotone set function μ: 𝒫(X)→