序列型空间的一个特征刻划

A CRJTERION OF SEQUENTIAL SPACES

本文证明了拓扑向量空间E是序列型空间的一个特征为：（1）E的每个序列开集都是开集；（2）取值于E中的任意无穷矩阵（xij）i,j,若对每个j均有limxij=xj，并且limxj=x,则一定存在严格递增序列（ik）和（jk）使得limxikjk=x.作为应用证明了序列型A-空间必是k-空间．

in this paper, it is proved that the criterion for a topological vector space Eto be a sequential space is: (1) every sequentially open set of E is an open set; (2) for everyinfinite matrix (xij)i,j of E, if lim xij= xj (j = 1, 2,…) and lim xj = x, then there are strictlyincreasing sequences (ik) and (jk) such that lim xikjk = x. As its application, we prove thatevery sequential A-space must be K-space.