Cantor algebra
In mathematics, a Cantor algebra, named after
countable and one complete
.
The countable Cantor algebra is the Boolean algebra of all
clopen subsets of the Cantor set. This is the free Boolean algebra
on a countable number of generators. Up to isomorphism, this is the only nontrivial Boolean algebra that is both countable and atomless.
The complete Cantor algebra is the complete Boolean algebra of
meager sets (Balcar & Jech 2006). It is isomorphic to the completion of the countable Cantor algebra. (The complete Cantor algebra is sometimes called the Cohen algebra, though "Cohen algebra" usually refers to a different type of Boolean algebra.) The complete Cantor algebra was studied by von Neumann in 1935 (later published as (von Neumann 1998)), who showed that it is not isomorphic to the random algebra
of Borel subsets modulo measure zero sets.