Cross-complementary subsets in paratopologicalgroups

Temel Bulgular & Veri:Tkachenko [TopologicalGroups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about theabove question in paratopological groups [Open problem 4.6.9, Topological Groups andRelated Structures, Atlantis Press, World Sci. 2008].

💡

Sonuç & Katkı:Arhangel’skiˇı’s results hold fork-gentle paratopological groups.

🔬Tür:Araştırma Makalesi

📍Kapsam:2003 Verileri

⚙️Değişkenler:Alan Parametreleri

Abstract

The following general question is considered by A.V. Arhangel’skiˇı [Perfect mappings intopological groups, cross-complementary subsets and quotients, Comment. Math. Univ.Carolin. 2003]. Suppose thatGis a topological group, andF, Mare subspaces ofGsuchthatG=M F. Under these general assumptions, how are the properties ofFandMrelated to the properties ofG? Also, A.V. Arhangel’skiˇı and M. Tkachenko [TopologicalGroups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about theabove question in paratopological groups [Open problem 4.6.9, Topological Groups andRelated Structures, Atlantis Press, World Sci. 2008]. In this paper, we mainly considerthis question and some positive answers to this question are given. In particular, we findmany A.V. Arhangel’skiˇı’s results hold fork-gentle paratopological groups.

🔖

Bu Makaleye Atıf Yap

LİN, W., FANG, L., XİE, L. (2022). Cross-complementary subsets in paratopologicalgroups. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 1–7. https://ajindex.com/articles/529587

📄 Tam Metin PDF Okuyucu

Yeni Sekmede Aç ↗

↗Yeni Sekme

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (1)

A.V. Arhangel’skiˇı,Perfect mappings in topological groups, cross-complementary sub-sets and quotients, Comment. Math. Univ. Carolin.44, 4, 701–709, 2003. [2]A.V. Arhangel’skiˇı and V.I. Ponomarev,Fundamentals of General Topology: Problemsand Exercises, Reidel, 1984. [3]A.V. Arhangel’skiˇı 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,OnH-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.