## Generalized free products

### Volume 88 / 2001

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

#### Abstract

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.