Topological Proofs of Some Rasiowa-Sikorski Lemmas.
We give topological proofs of Görnemann's adaptation to Heyting algebras of the Rasiowa-Sikorski
Lemma for Boolean algebras; and of the Rauszer-Sabalski generalisation of it to distributive
lattices.
The arguments use the Priestley topology on the set of prime filters, and the Baire category theorem.
This is preceded by a discussion of criteria for compactness of various spaces of subsets of a
lattice, including spaces of filters, prime filters etc.