HyperFunction and SuperHyperFunction in Chemistry

Abstract

Hyperstructures and their hierarchical extensions, the Superhyperstructures, furnish a flexible framework
for modelling multilayered phenomena across a wide range of disciplines. Viewed through the lens of
functions, these ideas manifest as HyperFunctions and SuperHyperFunctions, whose values belong to
iterated powersets rather than to ordinary codomains. Although the structural and computational aspects
of hyperstructures have been explored well beyond mathematics—including notable work in chemistry—the
corresponding functional counterparts remain largely unexamined in that context. To address this gap,
the present paper introduces several precise definitions of HyperFunctions and SuperHyperFunctions
tailored to chemical systems and investigates their fundamental properties. These set-valued constructs
capture nested reactivity patterns and multi-step pathways, thereby opening new avenues for describing
complex chemical processes.