Lattice of compactifications of a topological group

Categories and General Algebraic Structures with Applications

Zhiqiang Xiao¹  Wei He² 

[1] Department of Mathematics, Nanjing Normal University, Nanjing, 210046, China.;Institute of Mathematics, Nanjing Normal University;

关键词: Topological group;    compactification of a topological group;    complete lattice;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown