The Lee identities in topoi. I (Q1368589)

This paper investiges the so-called Lee identities for topoi. These are weaker than de Morgan's law. The author first discusses these identities in the context of compact, Hausdorff spaces, generalizing the results known for de Morgan's law on the topological setting. He then considers these identities in a topos \({\mathcal E}\), relating them to statements about maximal and prime ideals and filters for commutative rings, distributive lattices and Boolean algebras in \({\mathcal E}\).