On the algebra of regular sets

AbstractThe mereotopology RT  − has in Stonian p-ortholattices its algebraic counterpart. We study representability of these lattices and show that not all Stonian p-ortholattices can be represented by the set of regular sets of a topological space. We identify five conditions that hold in algebras of regular sets and which can be used to eliminate non-representable Stonian p-ortholattices. This shows not only that the original completeness theorem for RT  − is incorrect, but is also an important step towards an algebraic representation (up to isomorphism) of the regular sets of topological spaces.