Continuous lattices and Whiteheadian theory of space

Thomas Mormann

DOI: http://dx.doi.org/10.12775/LLP.1998.002

Abstract


In this paper a solution ofWhitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers Qyielding the real numbers R. The argument of the paper relies on the theories of continuous lattices and “pointless” topology.

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References


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