Mereocompactness and Duality for Mereotopological Spaces
Mereotopology studies relations between regions of space, including the contact relation.
It leads to an abstract notion of Boolean contact algebra which has been shown to be representable
as an algebra of regular closed subsets of a compact topological space. Here we define
mereotopological spaces and their mereomorphisms, and construct a dual equivalence between
the category of Boolean contact algebras and a category of mereotopological spaces that
have a property we call mereocompactness, strictly stronger than ordinary compactness.
This is a further illustration of the kind of duality that has been widely used in the
semantic analysis of propositional logics, and which has been a significant theme in the
research of J. Michael Dunn.