Cross-complementary subsets in paratopological groups

Authors : Weihua LİN, Lianhua FANG, Li-hong XİE

Pages : 1-7

Doi:10.15672/HJMS.2018.647

View : 16 | Download : 6

Publication Date : 2020-02-06

Article Type : Research Paper

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