Partitions of totally disconnected compact spaces (in Russian)

Abstract

In the paper is studied the connection between subalgebras of a Boolean algebra and partitions of the corresponding Stone space (totally disconnected compact space). In case of extremally disconnected space it is proved that regularly embedded subalgebras correspond exactly to continuous partitions (in the sense of K. Kuratoyski). The concepts of a weight of a Boolean algebra and of a weight of a partition are studied.