A topolinguistic space is a triple

L := (X, τ, Σ)
where:

X is a nonempty set whose elements are called linguistic states (utterances, propositions, clauses, or semantic tokens).
τ is a topology on X, whose open sets represent semantic neighborhoods, i.e. collections of states mutually reachable by small interpretive variation.
Σ is a stratification of X into disjoint layers Σ = {X₀, X₁, X₂, …}, corresponding respectively to syntactic, semantic, pragmatic, and institutional levels.
The stratification is required to satisfy:

X = ⋃ₖ Xₖ , Xᵢ ∩ Xⱼ = ∅ for i ≠ j
and each stratum Xₖ inherits the subspace topology from (X, τ).

C.2 Semantic Continuity and Morphisms
Let (X, τ, Σ) and (Y, σ, Π) be topolinguistic spaces. A topolinguistic morphism is a function

f : X → Y
satisfying:

Continuity: f is continuous with respect to τ and σ.
Stratum-respect: for each k, f(Xₖ) ⊆ Yₖ or Yₖ₊₁.
This permits upward semantic transport (e.g. syntax → semantics) while forbidding unstructured collapse (e.g. law → raw syntax).

Composition of such morphisms is associative, and identity maps exist. Therefore, topolinguistic spaces form a category TopLing.