The simplicial complexes of a relation have a star structure which is richer than the usual q-connectivity structure of Q-analysis. A mathematical theory of stars is developed in which the star and hub mappings are analogous to a Galois pair. Parameters can be associated with the new structures which have q-nearness and q-connectivity as a special case. These ideas clarify the notion of t-force and resolve various problems in shomotopy analysis. Stars and hubs form isomorphic lattices analogous to Ho's Galois lattice construction. It is argued that the theory of stars will enrich the hierarchical backcloth-traffic theory of Q-analysis, and improve its value as an applied methodology.
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