一致空间中的群结构

Group Structure in Uniform Space

一致空间作为介于拓扑空间与度量空间之间的一类空间,它与拓扑空间和度量空间有着密切的联系,从群这个侧面去研究了一致空间的代数特征,在一致结构上建立了群结构,讨论了它与一致空间和拓扑群的联系,即当拓扑中有群结构时,便可产生一致结构,并给出了一致空间的同态定理,这为进一步探讨拓扑空间以及度量空间的关系和结构创造了一定的条件。

Uniform space is a kind of space between topological space and metric space.Uniform space is also a kind space highly related with topological space and metric space.We employed,group and homomorphism to research this relation and reveal algebraic character of uniform space.We also discussed the relation between topological group and uniformity to provide some conditions for further study.