UNIFORM ALGEBRAS IN THE CANTOR AND BAIRE SPACES

For each pointclassP (2 ! ) dene U() as the collection of all X 2 ! such that the preimage f 1 (X) belongs to for each continuous f : 2 ! ! 2 ! . We study the properties of and possible rela- tionships among the classes U(), where ranges over the -algebras (l), (m), the completely Ramsey sets, and the sets with the Baire prop- erty. We also prove some results about cardinal coecients of U() for the general case of Marczewski-Burstin representable -algebras . We nish