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An inverse limit representation for complete Boolean algebras
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 164-166

Voir la notice de l'article provenant de la source Cambridge University Press

There are two well-known methods to build up algebras from given algebras, the direct and inverse limits, and a systematic account of these constructions may be found in [2]. It is known that every algebra can be represented as a direct limit of finitely generated algebras although in some cases the representation is trivial. Furthermore, Haimo [3] has established a certain inverse limit representation for the class of all infinite Boolean algebras which generalises, in actual fact, to the class of all infinite lattices with 1. The purpose of this note is to exhibit a certain nontrivial inverse limit representation which is peculiar to the class of infinite, complete Boolean algebras. 
Beazer, R. An inverse limit representation for complete Boolean algebras. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 164-166. doi: 10.1017/S0017089500001609
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[1] 1.Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloqium Publications Vol. 25, 3rd edition (Providence, R. I., 1967). Google Scholar

[2] 2.Grätzer, G., Universal Algebra (New York, 1968). Google Scholar

[3] 3.Haimo, F., Some limits of Boolean algebras. Proc. Amer. Math. Soc. 2 (1951), 566–576. Google Scholar | DOI

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