关于几乎拓扑群的注记

A Note on Almost Topological Groups

中文关键词:  几乎拓扑群  次可度量  $\lambda$-narrow  可分

英文关键词:almost topological group  submetrizable  $\lambda$-narrow  separable

中文摘要:

      本文主要讨论了有关几乎拓扑群的度量性和基数不变量,并给出了几乎拓扑群是拓扑群的条件,证明了: (1)具有可数$\pi$-特征的几乎拓扑群是次可度量的; (2)任意的左$\lambda$-narrow几乎拓扑群是$\lambda$-narrow的; (3)所有可分的几乎拓扑群是$\omega$-narrow的.最后在文中提出了一些问题.

英文摘要:

      In this paper, we mainly discuss some generalized metric properties and the cardinal invariants of almost topological groups. We give a characterization for an almost topological group to be a topological group and show that: (1) Each almost topological group that is of countable $\pi$-character is submetrizable; (2) Each left $\lambda$-narrow almost topological group is $\lambda$-narrow; (3) Each separable almost topological group is $\omega$-narrow. Some questions are posed.