Afrika Matematika

, Volume 30, Issue 1–2, pp 345–353 | Cite as

One point compactification of generalized topological spaces

  • Ganesan ChinnaramanEmail author
  • Muruga Jothi Ramachandran


The notions of a s-\(T_1\) space, an almost generalized Hausdorff space, and a \(\mu \)-locally compact space in the context of generalized topological spaces are introduced. Properties in relation to these spaces are established. Finally, a version of one point compactification of a s-\(T_1\) space is obtained.


Generalized topological spaces One point compactification \(\mu \)-separation \(\mu \)-compact \(\mu \)-locally compact 

Mathematics Subject Classification

54A05 54D35 54D45 



The authors thank the referee for his/her many valuable comments and suggestions towards the improvement of this paper.


  1. 1.
    Baro, E., Otero, M.: Locally definable homotopy. Ann. Pure Appl. Logic 161, 488–503 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Császár, Á.: Generalized topology, generalized continuity. Acta. Math. Hung. 96(4), 351–357 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Császár, Á.: \(\gamma \)-connected sets. Acta. Math. Hung. 101(4), 273–279 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Császár, Á.: Extremally disconnected generalized topologies. Ann. Univ. Bp. Sect. Math. 47, 151–161 (2004)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Császár, Á.: Normal generalized topologies. Acta. Math. Hung. 115(4), 309–313 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Császár, Á.: Separation axioms for generalized topologies. Acta. Math. Hung. 104, 63–69 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Delfs, H., Knebusch, M.: Locally Semialgebraic Spaces, Lecture Notes in Math. Springer, New York (1985)CrossRefzbMATHGoogle Scholar
  8. 8.
    Edmundo, M., Prelli, L.: Sheaves on \(\cal{T}\)-topologies. J. Math. Soc. Jpn. 68(1), 347–381 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ganesan, C., Muruga Jothi, R.: A note on \(\vartheta \)-topological spaces. Quest. Answ. Gen. Topol. (to appear)Google Scholar
  10. 10.
    Munkres, J.R.: Topology, 2nd edn. PHI Learning Pvt Ltd, New Delhi (2012)zbMATHGoogle Scholar
  11. 11.
    Thomas, J., John, S.J.: \(\mathfrak{g}\)-compacness in generalized topological spaces. J.Adv. Stud. Topol. 3(3), 18–22 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Knebusch, M.: Weakly Semialgebraic Spaces, Lecture Notes in Math. Springer, New York (1989)CrossRefzbMATHGoogle Scholar
  13. 13.
    Li, Z., Lin, F.: Baireness on generalized topological spaces. Acta Math. Hung. 139(4), 320–336 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Min, W.K.: Almost continuity on generalized toplogical spaces. Acta. Math. Hung. 125(1–2), 121–125 (2009)CrossRefGoogle Scholar
  15. 15.
    Min, W.K.: On weak neighborhood systems and spaces. Acta. Math. Hung. 121(3), 283–292 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Min, W.K.: Remarks on separation axioms on generalized topological spaces. J. Chungcheong Math. Soc. 23(2), 293–298 (2010)Google Scholar
  17. 17.
    Piekosz, A.: On generalized topological spaces I. Ann. Math. Pol. 107(3), 217–241 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Piekosz, A.: On generalized topological spaces II. Ann. Math. Pol. 108(2), 185–214 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Piekosz, A., Wajch, E.: Compactness and compactifications in generalized topology. Topol. Appl. 194, 241268 (2015)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Shen, R.X.: A note on generalized connectedness. Acta. Math. Hung. 122(3), 231–235 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Wu, X., Zhu, P.: A note on \(\beta \)-connectedness. Acta. Math. Hung.
  22. 22.
    Xun, G.E., Ying, G.E.: \(\mu \)-Separations in generalized topological spaces. Appl. Math. J. Chin. Univ. 25(2), 243–252 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsV. H. N. S. N. College (Autonomous)VirudhunagarIndia
  2. 2.Department of MathematicsMadurai Kamaraj University Constituent CollegeSatturIndia

Personalised recommendations