$\mathbb{R}$ -可分解的仿拓扑群的连续$d$ -开同态象和子群
The continuous $d$-open homomorphism images and subgroups of $\mathbb{R}$-factorizabile paratopological groups
摘要：
本文证明了：（1）设$f:G\rightarrow H$是一个连续的$d$ -开满同态，若$G$是一个$\mathbb{R}$ -可分解的仿拓扑群，则$H$也是.改进了Peng和Zhang的结果\cite [定理1.7]{PZ}. (2)设$G$是正则$\mathbb{R}$ -可因子分解的仿拓扑群，则$G$的每个子群$H$是$\mathbb{R}$ -可因子分解的当且仅当$H$是嵌入在$G$中的$z$ -.这一结果对M.~ Sanchis和M.~ Tkachenko \cite [问题5.3]{ST}。
英文摘要：
In this paper, we prove that: (1) Let $f:G\rightarrow H$ be a continuous $d$-open surjective homomorphism; if $G$ is an $\mathbb{R}$-factorizabile paratopological group, then so is $H$. Peng and Zhang's result \cite[Theorem 1.7]{PZ} is improved. (2) Let $G$ be a regular $\mathbb{R}$-factorizable paratopological group; then every subgroup $H$ of $G$ is $\mathbb{R}$-factorizable if and only if $H$ is $z$-embedded in $G$. This result gives out a positive answer to an question of M.~Sanchis and M.~Tkachenko \cite[Problem 5.3]{ST}.
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