Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585310120190101Lattice of compactifications of a topological group395061406ENWei HeInstitute of Mathematics, Nanjing Normal UniversityZhiqiang XiaoDepartment of Mathematics, Nanjing Normal University, Nanjing, 210046, China.Journal Article20171205We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological group are obtained.http://cgasa.sbu.ac.ir/article_61406_5c0d76f764a8ff7460747ef9016d1a97.pdf