@article{article_504551, title={Cross-complementary subsets in paratopological groups}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={49}, pages={1–7}, year={2020}, DOI={10.15672/HJMS.2018.647}, author={Lin, Weihua and Fang, Lianhua and Xie, Li-hong}, keywords={metrizable groups,paratopological groups,$k$-gentle paratopological groups,perfect mappings,paracompact $p$-spaces,countable tightnesses}, 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. <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">Arhangel’skii </span> 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. <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">Arhangel’skii </span>’s results hold for $k$-gentle paratopological groups.}, number={1}, publisher={Hacettepe University}