Chemical Reactions as Topological Hyperstructures: A Topological Reformulation of the Hyperstructural Model of Redox Reactions

The hyperstructural model of redox reactions organises the oxidation states of an element into an H_v-group whose hyperoperation returns the set of thermodynamically accessible products. We recast this model in the language of general topology. To every hyperoperation ⊕ on a nite set H we attach a topology τ_⊕, the reaction topology, generated by the family of hyperproducts {x ⊕ y} as a subbasis. We prove that τ_⊕ is an Alexandrov topology whose minimal neighbourhoods are N(x) = ∩ {x ⊕ y : x ∈ x ⊕ y}; that its specialisation preorder admits the chemical reading y accompanies x in every reaction product containing x''; that τ_⊕ is T₀ exactly when no two species are reactionindistinguishable, and discrete exactly when every species is separated from all others by some reaction; and that the connected components of (H, τ_⊕) are the components of the comparability graph of that preorder. We then show that the hyperoperation is continuous for the Vietoris hyperspace topology whenever it is constant on minimal neighbourhoods, so that every H_v-group with discrete reaction topology is a topological H_v-group, and that the quotient by the fundamental relation β^∗ is discrete if and only if the β^∗-classes are open. The constructions are worked out on the redox data for tin, iron, copper and manganese: the hypergraphs induced by the iron H_v-group yield, respectively, a disconnected space with components {Fe³⁺} and {Fe, Fe²⁺}, a connected T₀ space, a connected non-T₀ space with two Kolmogorov classes, and an indiscrete space, while the copper hypergraph yields a connected, non-discrete T₀ space.