Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 1, 1 - 7, 06.02.2020
https://doi.org/10.15672/HJMS.2018.647

Öz

Kaynakça

  • [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.

Cross-complementary subsets in paratopological groups

Yıl 2020, Cilt: 49 Sayı: 1, 1 - 7, 06.02.2020
https://doi.org/10.15672/HJMS.2018.647

Öz

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.

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Weihua Lin Bu kişi benim 0000-0001-7866-7460

Lianhua Fang Bu kişi benim 0000-0002-3176-0470

Li-hong Xie Bu kişi benim 0000-0001-5584-2924

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA Lin, W., Fang, L., & Xie, L.-h. (2020). Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics, 49(1), 1-7. https://doi.org/10.15672/HJMS.2018.647
AMA Lin W, Fang L, Xie Lh. Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):1-7. doi:10.15672/HJMS.2018.647
Chicago Lin, Weihua, Lianhua Fang, ve Li-hong Xie. “Cross-Complementary Subsets in Paratopological Groups”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 1-7. https://doi.org/10.15672/HJMS.2018.647.
EndNote Lin W, Fang L, Xie L-h (01 Şubat 2020) Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics 49 1 1–7.
IEEE W. Lin, L. Fang, ve L.-h. Xie, “Cross-complementary subsets in paratopological groups”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 1–7, 2020, doi: 10.15672/HJMS.2018.647.
ISNAD Lin, Weihua vd. “Cross-Complementary Subsets in Paratopological Groups”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 1-7. https://doi.org/10.15672/HJMS.2018.647.
JAMA Lin W, Fang L, Xie L-h. Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics. 2020;49:1–7.
MLA Lin, Weihua vd. “Cross-Complementary Subsets in Paratopological Groups”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 1-7, doi:10.15672/HJMS.2018.647.
Vancouver Lin W, Fang L, Xie L-h. Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):1-7.