Geodesic
Representations of topological spaces on Boolean algebras of regular open sets
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 305-321 
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/
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     title = {Representations of topological spaces on {Boolean} algebras of regular open sets},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] G. Birkgof, Teoriya struktur, IL, Moskva, 1952

[2] H. de Vries, Compact spaces and compactifications in algebraic approach, Amsterdam, 1962 | Zbl

[3] B. Jonsson, “A Boolean algebra without proper automorphisms”, Proc. Amer. Math. Soc., 2 (1951), 766–770 | DOI | MR | Zbl

[4] V. V. Pashenkov, “O teoreme Stouna”, DAN SSSR, 194:4 (1970), 778–781 | Zbl

[5] V. V. Pashenkov, “O kompanentnykh chastichno uporyadochennykh mnozhestvakh”, Matem. zametki, 9:3 (1971), 275–283 | Zbl

[6] B. A. Efimov, “Diadicheskie bikompakty”, Trudy Mosk. matem. ob-va, XIV (1965), 211–247 | MR

[7] R. Sikorskii, Bulevy algebry, izd-vo «Mir», Moskva, 1969 | MR