Generalized free products
Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 175-192
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
J. D. Monk 1
@article{10_4064_cm88_2_2,
author = {J. D. Monk},
title = {Generalized free products},
journal = {Colloquium Mathematicum},
pages = {175--192},
year = {2001},
volume = {88},
number = {2},
doi = {10.4064/cm88-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm88-2-2/}
}
J. D. Monk. Generalized free products. Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 175-192. doi: 10.4064/cm88-2-2
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