Inclusion hyperspaces and capacities on Tychonoff spaces: functors and monads

TL;DR

This paper extends the inclusion hyperspace and capacity functors, along with their monads, from compact Hausdorff spaces to Tychonoff spaces, exploring their properties and applications.

Contribution

It introduces and analyzes the extension of inclusion hyperspace and capacity functors, including monads, to the broader category of Tychonoff spaces, expanding their theoretical framework.

Findings

Properties of inclusion hyperspaces on Tychonoff spaces are characterized.

Capacities on Tychonoff spaces are studied as non-additive measures.

Functor and monad structures are successfully extended to Tychonoff spaces.

Abstract

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.