Premium
Modular Interval Spaces
Author(s) -
Bandelt H.J.,
van de Vel M.,
Verheul E.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931630117
Subject(s) - mathematics , modular design , modular form , pure mathematics , metric space , linear subspace , generalization , modularity (biology) , interval (graph theory) , type (biology) , discrete mathematics , algebra over a field , combinatorics , mathematical analysis , computer science , ecology , biology , genetics , operating system
Modular interval spaces represent a common generalization of Banach spaces of type L 1 (μ) or B(X) , of hyperconvex metric spaces, modular lattices, modular graphs, and median algebras. It turns out that several types of structures are susceptible for a notion capturing essential features of modularity in lattices, e.g., semilattices, multilattices, metric spaces, ternary algebras, and graphs. There is no perfect correspondence between modular structures of various types unless the existence of a neutral point is imposed. Modular structures with neutral points embed in modular lattices. Particular modular interval spaces (e.g., median spaces, or more generally, modular spaces in which intervals are lattices) can be characterized by forbidden subspaces.