Time, topology and physical geometry

Abstract
The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes space
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    Cian Dorr (2011). Physical Geometry and Fundamental Metaphysics. Proceedings of the Aristotelian Society 111 (1pt1):135-159.
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