摘要
本文揭示了Banach压缩映象原理与空间完备性的关系,证明了在具有一致局部连通性的距离空间中,压缩映象原理与空间完备性仍然等价.
In this paper, we study a further relation between the Banach contraction principle and the completeness of spaces. We prove that for a metric space with uniformly local connectedness the Banach contraction principle is equivalent to the completeness.
出处
《系统科学与数学》
CSCD
北大核心
1997年第4期307-310,共4页
Journal of Systems Science and Mathematical Sciences
关键词
压缩映象原理
完备性
距离空间
巴拿赫
Contraction principle, completeness, uniformly local connectedness, metric space
