Graded inclusion and point-free geometry

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Giangiacomo Gerla
Annamaria Miranda
Title: Graded inclusion and point-free geometry
Journal: International Journal of Pure and Applied Mathematics
Volume 11
Pages: 63-81
Year: 2004


Point-free geometry is based on an idea of Whitehead in which one assumes as primitives the notions of region and inclusion relation. The points are defined by suitable abstraction processes, i.e. sequences of order-reversing functions. In the paper one observes that there are several difficulties in such an approach. These difficulties are avoided provided that the inclusion relation is substituted by a graded inclusion and therefore Whitehead's theory is considered in the framework of multi-valued logic.