On the algebra of regular sets
Properties of representable Stonian p-ortholattices
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Abstract
The 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.
Keywords
Regular sets Stonian p-ortholattice Representation Region-based topology Mereotopology Interior operation Localized distributivityMathematics Subject Classifications (2010)
Primary 54H10; Secondary 06B15 06E75 68T27 68T30 06B20 06E15Preview
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