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## Cross-complementary subsets in paratopological groups

#### Weihua LİN [1] , Lianhua FANG [2] , Li-hong XİE [3]

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.
metrizable groups, paratopological groups, $k$-gentle paratopological groups, perfect mappings, paracompact $p$-spaces, countable tightnesses
• [1] A.V. Arhangel’skii, Perfect mappings in topological groups, cross-complementary sub- sets and quotients, Comment. Math. Univ. Carolin. 44, 4, 701–709, 2003.
• [2] A.V. Arhangel’skii and V.I. Ponomarev, Fundamentals of General Topology: Problems and Exercises, Reidel, 1984.
• [3] A.V. Arhangel’skii and M. Tkachenko, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008.
• [4] N. Bourbaki, Elements de Mathematique, Premiere Partie, Livre 3, Ch. 3, 3-me ed., Hermann, Paris, 1949.
• [5] R. Engelking, General Topology, Revised and completed edition, Heldermann Verlag, 1989.
• [6] V.V. Filippov, On perfect images of paracompact p-spaces, Soviet Math. Dokl. 176, 533–536, 1967.
• [7] P. Li and L. Mou, On quasitopological groups, Topology Appl. 161, 243–247, 2014.
• [8] O. Ravsky, On H-closed paratopological groups, Visnyk Lviv. Univ. Ser. Mat. Mekh. 59, 96–101, 2001.
• [9] O. Ravsky, The topological and algebraic properties of paratopological groups, Ph.D. thesis. Lviv University, 2003 (in Ukrainian).
• [10] W. Roelke and S. Dierolf, Uniform Structures on Topological Groups and Their Quo- tients, McGraw-Hill, New York, 1981.
• [11] M. Tkachenko, Paratopological and semitopological groups vs topological groups, in: K.P. Hart, J. van Mill, P. Simon (Eds.), Recent Progress in General Topology III, Springer Atlantis Press, 803–859, 2013.
Primary Language en Mathematics Mathematics Orcid: 0000-0001-7866-7460Author: Weihua LİN Institution: Fujian Normal UniversityCountry: China Orcid: 0000-0002-3176-0470Author: Lianhua FANG Institution: Quanzhou University of Information EngineeringCountry: China Orcid: 0000-0001-5584-2924Author: Li-hong XİE (Primary Author)Institution: Wuyi UniversityCountry: China Publication Date : February 6, 2020
 Bibtex @research article { hujms504551, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1 - 7}, doi = {10.15672/HJMS.2018.647}, title = {Cross-complementary subsets in paratopological groups}, key = {cite}, author = {LİN, Weihua and FANG, Lianhua and XİE, Li-hong} } APA LİN, W , FANG, L , XİE, L . (2020). Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 1-7 . DOI: 10.15672/HJMS.2018.647 MLA LİN, W , FANG, L , XİE, L . "Cross-complementary subsets in paratopological groups". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1-7 Chicago LİN, W , FANG, L , XİE, L . "Cross-complementary subsets in paratopological groups". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1-7 RIS TY - JOUR T1 - Cross-complementary subsets in paratopological groups AU - Weihua LİN , Lianhua FANG , Li-hong XİE Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2018.647 DO - 10.15672/HJMS.2018.647 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1 EP - 7 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.647 UR - https://doi.org/10.15672/HJMS.2018.647 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Cross-complementary subsets in paratopological groups %A Weihua LİN , Lianhua FANG , Li-hong XİE %T Cross-complementary subsets in paratopological groups %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2018.647 %U 10.15672/HJMS.2018.647 ISNAD LİN, Weihua , FANG, Lianhua , XİE, Li-hong . "Cross-complementary subsets in paratopological groups". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 1-7 . https://doi.org/10.15672/HJMS.2018.647 AMA LİN W , FANG L , XİE L . Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 1-7. Vancouver LİN W , FANG L , XİE L . Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 7-1.

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