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A Pointless Theory of Space Based on Strong Connection and Congruence

We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological properties: mereology is described by a parthood relation satisfying the axioms of Closed Extensional Mereology; topology is described by means of a "simple region" predicate, by which a relation of “strong connection” between regions having at least a surface in common is defined; morphology is described by means of a "congruence" primitive, whose axioms exploit Tarski's analogy between points and spheres.