Knowledge libraries and information space

This research describes and develops Knowledge Libraries, idealised systems for organising and presenting information. By providing a mathematical basis, the definition of information space establishes a formal foundation for Knowledge Libraries. The definition of information space builds on the new definitions of L-collections, which generalise sets by allowing a real valued grade to be associated with each element, and set space, which generalises metric space to better model the relationships between information units. The multiple search tree method improves existing metric space range query algorithms. These algorithms are also generalised to work over set space. The sequential-hybrid algorithm enables efficient range queries over multi-dimensional spaces.