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.
Goldblatt, R., & Grice, M. (2016). Mereocompactness and Duality for Mereotopological Spaces. In Outstanding Contributions to Logic (Vol. 8, pp. 313–330). Springer. https://doi.org/10.1007/978-3-319-29300-4_15