局部Cauchy列的一个等价条件

An Equivalence of Locally Cauchy Sequence

局部凸分离空间(X,T)中序列(xn)是局部Cauchy列当且仅当存在单调增且趋于正无穷大的正实数列(an),使得min{an,am}(xn-xm)?T?→0(m,n→∞),并得到了一些相关的结论.

The sequence(x n) in lcs(locally convex separated space)(X,T) is locally Cauchy sequence if and only if there is an increasing unbounded sequence of positive real numbers(a n) such that min{a n,am}(xn? xm)??T→0(m,n→∞).(X,T)is locally complete if and only if the closed absolutely convex hull of every locally sequence in(X,T) is compact.