拓扑群范畴研究的若干进展

Some Progresses on the Category of Topological Groups

拓扑群是拓扑代数领域的重要研究对象,在调和分析、动力系统等领域有广泛的应用.拓扑群和连续群同态范畴具有许多重要且有趣的性质.介绍从范畴论角度研究拓扑群范畴的若干进展.内容涉及拓扑群范畴的基本性质、拓扑群范畴的准紧反射、紧反射(Bohr紧化)、Raǐkov完备反射(Raǐkov完备化)、C-紧拓扑群、c-完备态射等.

Topological groups are important research objects in the field of topological algebras,and they are applied to many fields such as harmonic analysis,dynamic systems,etc.The category of topological groups has many interesting properties.This paper is a survey of some results on the category of topological groups.The content includes some basic categorical properties,the precompact reflections of topological groups,the compact reflections of topological groups （the Bohr compactification）,Raǐkov completions,C-compact groups and c-proper homomorphisms.