A Connection Based Approach to Common-sense Topological Description and Reasoning

The standard mathematical approaches to topology, point-set topology and algebraic topology, treat points as the fundamental, undefined entities, and construct extended spaces as sets of points with additional structure imposed on them. Point-set topology in particular generalises the concept of a `space' far beyond its intuitive meaning. Even algebraic topology, which concentrates on spaces built out of `cells' topologically equivalent to n-dimensional discs, concerns itself chiefly with rather abstract reasoning concerning the association of algebraic structures with particular spaces, rather than the kind of topological reasoning which is required in everyday life, or which might illuminate the metaphorical use of topological concepts such as `connection' and `boundary'. This paper explores an alternative to these approaches, RCC theory, which takes extended spaces (`regions') rather than points as fundamental. A single relation, C (x; y) (read `Region x connects with reg...