Free Boolean Topological Groups

Free and free Abelian topological groups are traditional objects of research in topological algebra. Free Boolean topological groups have been much less investigated, although they arise fairly often in various studies (especially in the set-theoretic context) and have quite specific features. Thus, essentially, only Boolean groups can have extremal topological properties, such as extremal disconnectedness, irresolvability, maximality, and so on. Moreover, the topology of the free Boolean group on a countable filter is closely related to classical notions of forcing. This book collects known and new results on free Boolean topological groups. Special emphasis is placed on the application of set theory to Boolean topological groups and vice versa. The book is intended for anyone familiar with the basics of general topology and topological algebra.