Geodesic
Generalized free products
J. D. Monk1
1 Mathematics Department University of Colorado 395 UCB Boulder, CO 80309, U.S.A.
Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 175-192.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A subalgebra $B$ of the direct product $\prod _{i\in I}A_i$ of Boolean algebras is finitely closed if it contains along with any element $f$ any other member of the product differing at most at finitely many places from $f$. Given such a $B$, let $B^\star $ be the set of all members of $B$ which are nonzero at each coordinate. The generalized free product corresponding to $B$ is the subalgebra of the regular open algebra with the poset topology on $B^\star $ generated by the natural basic open sets. Properties of this product are developed. The full regular open algebra is also treated.
DOI : 10.4064/cm88-2-2
Keywords: subalgebra direct product prod boolean algebras finitely closed contains along element other member product differing finitely many places given star set members which nonzero each coordinate generalized product corresponding subalgebra regular algebra poset topology star generated natural basic sets properties product developed full regular algebra treated

J. D. Monk 1

1 Mathematics Department University of Colorado 395 UCB Boulder, CO 80309, U.S.A. 
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J. D. Monk. Generalized free products. Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 175-192. doi : 10.4064/cm88-2-2. http://geodesic.mathdoc.fr/articles/10.4064/cm88-2-2/

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