Generalized free products

Tom 88 / 2001

J. D. Monk Colloquium Mathematicum 88 (2001), 175-192 MSC: Primary 06E05. DOI: 10.4064/cm88-2-2


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.


  • J. D. MonkMathematics Department
    University of Colorado
    395 UCB
    Boulder, CO 80309, U.S.A.

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