A sequence of elements of a complete Boolean algebra (briefly c.B.a.) converges to a priori (in notation ) if . The sequential topology on is the maximal topology on such that implies , where denotes the convergence in the space — the a posteriori convergence.
These two forms of convergence, as well as the properties of the sequential topology related to forcing, are investigated. So, the a posteriori convergence is described in terms of killing of tall ideals on , and it is shown that the a posteriori convergence is equivalent to the a priori convergence iff forcing by does not produce new reals. A property () of c.B.a.’s, satisfying -cc -cc and providing an explicit (algebraic) definition of the a posteriori convergence, is isolated. Finally, it is shown that, for an arbitrary c.B.a. , the space is sequentially compact iff the algebra has the property () and does not produce independent reals by forcing, and that implies is the unique sequentially compact c.B.a. in the class of Suslin forcing notions.