对近似收敛数列空间A_c(R)性质的探讨

A Study for the Properties of the Approximate Convergent Sequence Space

从实数域上近似收敛数列空间Ac(R)定义出发,指出了收敛数列空间和近似收敛数列空间Ac(R)的包含关系和稠密性,介绍了近似收敛数列空间Ac(R)的一些基本性质,着重讨论了近似收敛数列空间Ac(R)的可分性及其对偶空间,最后又给出了近似收敛数列空间Ac(R)不是局部凸且不是局部有界的证明.

Based on the definition of approximate convergent sequence space Ac（R）,the denseness and the inclusion relationship between the convergent sequence space and approximate convergent sequence space Ac（R） are pointed out.Some basic properties of approximate convergent sequence space Ac（R） are introduced,and the separability of the space Ac（R） and its dual space are discussed.It is proved that approximate convergence sequence space Ac（R） is neither locally convex nor locally bounded.