k-非常光滑空间的若干新特征

Some New Characteristics of k-very Smooth Spaces

利用局部自反原理,获得k-非常光滑空间的一个新特征:X是k-非常光滑空间当且仅当对x∈S(X),有dimSx=rk且^x是X**的r-光滑点.此外,还深入研究了k-非常光滑空间,又得到了k-非常光滑空间的若干新特征.

A new characteristic of k-very smooth spaces is obtained by using the local reflexive theorem.X is k-very smooth spaces if and only if dimSx=r≤k and x is the r-smooth point of X^·· for any x ∈ S （X）. Besides, are obtained the k-very smooth spaces is studied and some new characteristics of k-very smooth spaces are obtained.