Advertisement

Journal of Mathematical Sciences

, Volume 188, Issue 2, pp 77–84 | Cite as

Topologizations of G-spaces

  • Taras Banakh
  • Igor Protasov
Article

Abstract

For a G-space X, we put and explore a question whether X admits a non-discrete Hausdorff G-invariant topology.

Keywords

G-space G-invariant topology filter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. I. Arnautov, “Nondiscrete topologizability of countable rings,” Dokl. Akad. Nauk SSSR, 191, 747–750 (1970).MathSciNetGoogle Scholar
  2. 2.
    T. Banakh, I. Protasov, and O. Sipacheva, Topologizations of Sets Endowed with an Action of Monoid, preprint available at ArXiv:1112.5729v1.Google Scholar
  3. 3.
    D. Dikranjan and I. Protasov, “Counting maximal topologies on countable groups and rings,” Topology Appl., 156, 322–325 (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    D. Dikranjan and D. Shakhmatov, “The Markov–Zariski topology of an Abelian group,” J. Algebra, 324, No. 6, 1125–1158 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    N. Hindman, I. Protasov, and D. Strauss, “Topologies on S determined by idempotents in βS,Topol. Proceed., 23, 155–190 (1998).MathSciNetGoogle Scholar
  6. 6.
    A. A. Klyachko and A. V. Trofimov, “The number of non-solutions of an equation in a group,” J. Group Theory, 8, No. 6, 747–754 (2005).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    A. A. Markov, “On unconditionally closed sets,” Mat. Sb., 18, No. 1, 3–28 (1946).Google Scholar
  8. 8.
    J. van Mill, “A note on Ford example,” Topol. Proceed., 28, 689–694 (2004).zbMATHGoogle Scholar
  9. 9.
    S. Morris and V. Obraztsov, “Nondiscrete topological groups with many discrete subgroups,” Topol. Appl., 84, 103–120 (1998).MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. Yu. Ol’shanskii, “A remark on a countable nontopologized group,” Vest. Mosk. Univ. Ser. I. Mat. Mekh., No. 3, 103 (1980).Google Scholar
  11. 11.
    A. Yu. Ol’shanskii, The Geometry of Defining Relations in Groups [in Russian], Nauka, Moscow, 1989.Google Scholar
  12. 12.
    I. V. Protasov, “Filters and topologies on semigroups,” Mat. Stud., 3, 15–28 (1994).MathSciNetzbMATHGoogle Scholar
  13. 13.
    I. V. Protasov, “Extremal topologies on groups,” Mat. Stud., 15, 9–22 (2001).MathSciNetzbMATHGoogle Scholar
  14. 14.
    I. V. Protasov, “Maximal topologies on groups,” Sib. Math. J., 39, 1368–1381 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    I. Protasov and E. Zelenyuk, Topologies on Groups Determined by Sequences, VNTL, Lviv, 1999.zbMATHGoogle Scholar
  16. 16.
    S. Shelah, “On a problem of Kurosh, Jo’nsson groups and applications,” Word Problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), North-Holland, Amsterdam, 1980, pp. 373–394.Google Scholar
  17. 17.
    A. V. Trofimov, “A theorem on embedding in nontopologizable groups,” Vest. Mosk. Univ. Ser. I. Mat. Mekh., No. 3, 60–62 (2005).Google Scholar
  18. 18.
    A. V. Trofimov, “A perfect nontopologizable group,” Vest. Mosk. Univ. Ser. I. Mat. Mekh., No. 1, 7–13 (2007).Google Scholar
  19. 19.
    Y. Zelenyuk, “On topologizing groups,” J. Group Theory, 10, No. 2, 235–244 (2007).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsLviv UniversityLvivUkraine
  2. 2.Department of CyberneticsKyiv UniversityKyivUkraine

Personalised recommendations