- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 1
- Cross-complementary subsets in paratopological groups
Cross-complementary subsets in paratopological groups
Authors : Weihua Lin, Lianhua Fang, Li-hong Xie
Pages : 1-7
Doi:10.15672/HJMS.2018.647
View : 11 | Download : 4
Publication Date : 2020-02-06
Article Type : Research
Abstract :The following general question is considered by A.V. Arhangel’skii [Perfect mappings in topological groups, cross-complementary subsets and quotients, Comment. Math. Univ. Carolin. 2003]. Suppose that $G$ is a topological group, and $F , M$ are subspaces of $G$ such that $G = MF$. Under these general assumptions, how are the properties of $F$ and $M$ related to the properties of $G$? Also, A.V. Arhangel’skii and M. Tkachenko [Topological Groups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about the above question in paratopological groups [Open problem 4.6.9, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008]. In this paper, we mainly consider this question and some positive answers to this question are given. In particular, we find many A.V. Arhangel’skii 's results hold for $k$-gentle paratopological groups.Keywords : metrizable groups, paratopological groups, $k$-gentle paratopological groups, perfect mappings, paracompact $p$-spaces, countable tightnesses