Arbitrarily large continuous algebras on one generator

Adámek, Jiří; Koubek, Václav; Nelson, Evelyn; Reiterman, Jan

doi:10.1090/S0002-9947-1985-0800258-7

Arbitrarily large continuous algebras on one generator
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by Jiří Adámek, Václav Koubek, Evelyn Nelson and Jan Reiterman

Trans. Amer. Math. Soc. 291 (1985), 681-699

DOI: https://doi.org/10.1090/S0002-9947-1985-0800258-7

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Abstract:

Generation of order-continuous algebras is investigated for various concepts of continuity. For the continuity understood as the preservation of joins of countably-directed sets, arbitrarily large infinitary continuous algebras on one generator are constructed.

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