Properties of representable Stonian p-ortholattices
Michael Winter, Torsten Hahmann, Michael Grüninger · 2012
The mereotopology RT − has in Stonian p-ortholattices its algebraic coun- terpart. 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.