Continuous Quivers of Type A (IV)

This if the final paper in series Continuous Quivers of Type A. In this part, we generalize existing geometric models type A cluster structures for new E-clusters introduced part (III). We also introduce an isomorphism theories and a weak equivalence theories. Examples both are given. use these isomorphisms to begin classifying continuous generalization mutation. encompasses mutation (infinite) sequences Then link our earlier models. Finally, space mutations which generalizes exchange graph structure, show that paths mutations.