Mereotopology without Mereology

Author(s)
Forrest, Peter
Publication Date
2010
Abstract
Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is 'interior parthood'. This choice will have the advantage that filters may be defined with respect to it, constructing "points", as Peter Roeper has done ("Region-based topology", 'Journal of Philosophical Logic', 26 (1997), 25–309). This paper generalizes Roeper's result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an 'approximate lattice', because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of "points" in a topological "space".
Citation
Journal of Philosophical Logic, 39(3), p. 229-254
ISSN
1573-0433
0022-3611
Link
Publisher
Springer Netherlands
Title
Mereotopology without Mereology
Type of document
Journal Article
Entity Type
Publication

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