Geodesic
Representations of topological spaces on Boolean algebras of regular open sets
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 305-321

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Every semiregular topological space is naturally homeomorphic to a suitably topologized set of certain filters of the Boolean algebra of its regular subsets. This homeomorphism is applied to the investigation of irreducible maps of compact spaces. The selected system of filters serves to induce a topology on the above Boolean algebra completely characterizing the original space. Bibliography: 7 titles. 
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     author = {V. V. Pashenkov},
     title = {Representations of topological spaces on {Boolean} algebras of regular open sets},
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V. V. Pashenkov. Representations of topological spaces on Boolean algebras of regular open sets. Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 305-321. http://geodesic.mathdoc.fr/item/SM_1973_20_3_a0/