MODULAR INTERVAL SPACES

Modular interval spaces represent a common generalization of Banach sp aces of type L1(mu) or B(X), of hyperconvex metric spaces, modular lat tices, modular graphs, and median algebras. It turns out that several types of structures are susceptible for a notion capturing essential f eatures of modularity in lattices, e.g., semilattices, multilattices, metric spaces, ternary algebras, and graphs. There is no perfect corre spondence between modular structures of various types unless the exist ence of a neutral point is imposed. Modular structures with neutral po ints embed in modular lattices. Particular modular interval spaces (e. g., median spaces, or more generally, modular spaces in which interval s and lattices) can be characterized by forbidden subspaces.