Lattice of compactifications of a topological group

Document Type: Research Paper


1 Institute of Mathematics, Nanjing Normal University

2 Department of Mathematics, Nanjing Normal University, Nanjing, 210046, China.


We 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.


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