Free Boolean Topological Groups

Abstract

Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.

Keywords

• free Boolean topological group
• free Boolean linear topological group
• free topological group
• free Abelian topological group
• almost discrete space
• Ramsey filter
• extremally disconnected group