Hausdorff空间中逐次叠代法的一点注记

<正> 设(S,τ)是一个拓扑空间,它满足Hausdorff分离公理,算子A作用于空间(S,τ),它变收敛序列为收敛序列,例如,A是拓扑空间(S,τ)中的连续映射。如所周知,从拓扑空间(S,τ)中某一个初始元x0∈(S,τ)出发,经过逐次叠代法

A Remark on Method of Successive Substitution in Hausdorff Space

Let A is a mapping which maps the Hausdorff topological space (S,τ)into itself, and satisfying a condition xm→x(m→+∞) always implies Axm→Ax. Consider the sequence xn=Axn-1(n=1, 2, 3,…), where x0 is some initial element. In this remark the following theore