Cross-complementary subsets in paratopological groups

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.

Keywords

metrizable groups paratopological groups $k$-gentle paratopological groups perfect mappings paracompact $p$-spaces countable tightnesses

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Cite This Article

LİN, W., FANG, L., XİE, L. (2020). Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 1–7. https://ajindex.com/articles/669289

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References (11)

A.V. Arhangel’skii, Perfect mappings in topological groups, cross-complementary sub- sets and quotients, Comment. Math. Univ. Carolin. 44, 4, 701–709, 2003
A.V. Arhangel’skii and V.I. Ponomarev, Fundamentals of General Topology: Problems and Exercises, Reidel, 1984
A.V. Arhangel’skii and M. Tkachenko, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008
N. Bourbaki, Elements de Mathematique, Premiere Partie, Livre 3, Ch. 3, 3-me ed., Hermann, Paris, 1949
R. Engelking, General Topology, Revised and completed edition, Heldermann Verlag, 1989
V.V. Filippov, On perfect images of paracompact p-spaces, Soviet Math. Dokl. 176, 533–536, 1967
P. Li and L. Mou, On quasitopological groups, Topology Appl. 161, 243–247, 2014
O. Ravsky, On H-closed paratopological groups, Visnyk Lviv. Univ. Ser. Mat. Mekh. 59, 96–101, 2001
O. Ravsky, The topological and algebraic properties of paratopological groups, Ph.D. thesis. Lviv University, 2003 (in Ukrainian)
W. Roelke and S. Dierolf, Uniform Structures on Topological Groups and Their Quo- tients, McGraw-Hill, New York, 1981
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.