关于${\cal I}$-覆盖映射与1-${\cal I}$-覆盖映射

On ${\mathcal{I}}$-Covering Mappings and 1-${\mathcal{I}}$-Covering Mappings

中文关键词:  理想收敛  ${\cal I}$-覆盖映射  1-${\cal I}$-覆盖映射  紧映射

英文关键词:ideal convergence  ${\mathcal{I}}$-covering mappings  1-${\mathcal{I}}$-covering mappings  compact mappings

中文摘要:

      本文介绍了${\cal I}$-覆盖映射与1-${\cal I}$-覆盖映射的概念,并通过一些例子说明序列覆盖映射与${\cal I}$-覆盖映射的区别. 应用这些概念,得到${\cal I}$-覆盖映射(1-${\cal I}$- 覆盖映射)的一些性质及度量空间的${\cal I}$-覆盖(1-${\cal I}$-覆盖映射)紧映像的一些特征.

英文摘要:

      In this paper, we introduce the concepts of ${\mathcal{I}}$-covering mappings and 1-${\mathcal{I}}$-covering mappings, discuss the difference between sequence-covering and ${\mathcal{I}}$-covering mappings by some examples. With those concepts, we get some interesting properties of ${\mathcal{I}}$-covering (1-${\mathcal{I}}$-covering) mappings and some characterizations of ${\mathcal{I}}$-covering (1-${\mathcal{I}}$-covering) and compact mapping images of metric spaces.