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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Cross-complementary subsets in paratopological groups

Weihua Lin(Fujian Normal University)0000-0001-7866-7460
Lianhua Fang(Quanzhou University of Information Engineering)0000-0002-3176-0470
Li-hong Xie(Wuyi University)0000-0001-5584-2924
Pages
—
Publication Date
2020-02-06
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Arhangel’skii 's results hold for $k$-gentle paratopological groups.

📌 3 Key Takeaways

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Objective & Hypothesis:The following general question is considered by A.V.
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Key Findings & Data: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].
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Conclusion & Impact:Arhangel’skii 's results hold for $k$-gentle paratopological groups.
🔬Design:Research Article
📍Scope:2003 Verileri
⚙️Variables:metrizable groups · paratopological groups · $k$-gentle paratopological groups

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.

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Cite This Article

Lin, W., Fang, L., Xie, L. (2020). Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/HJMS.2018.647

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References (11)

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