ISSN 2581-5954

International Journal of Modern Computation, Information and Communication Technology

April 2019, Vol. 2, Issue 4, p. 27-31.​​

On Normality in Dense Topological Subspaces
B. Ogola, O. Ongati, N. B. Okelo
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail:


A lot of studies have been conducted on dense topological spaces over a long period of time and interesting results have been obtained. Normality and compactness on topological spaces have also been investigated for decades however, characterization when the subspaces are particularly dense has not  been exhausted. In the present study, we consider the case when the countable subspaces are dense. We introduce the notion of normality in dense topological spaces Also, some characterizations and properties of these notions are investigated.

Keywords: Topological space; Normality; Denseness; Compactness.


  1. Achieng OE, Odongo D, Okelo NB. On Certain Properties of Identification Topological Subspaces. Int J Mod Comput Info and Commun Technol 2018;3(11):238-40.
  2. Amudhambigai B, Revathi GK, Hemalatha T, On Strongly b - d- Continuous M-Set Functions. Indian Streams Research Journal 2016;6(8):21-8
  3. Andrijevic D. On b-open sets. Mat Vesnik 1996;48:59-64.
  4. Andrijevic V. Semi-preopen sets. Mat. Vesnik 1986;38:24-32.
  5. Brooks F. Indefinite cut sets for real functions. Amer Math Monthly 1971;78: 1007-10.
  6. Change CL.  Fuzzy topological spaces. J Math Anal Appl 1968;24:182-90.
  7. Csaszar A. Generalized open sets. Acta. Math. Hungar 1997;75(2):65-87.
  8. Dontchev J, Przemski M. On the various decompositions of continuous and some weakly continuous. Acta Math Hung 1996; 71(1):109-20.
  9. Maheshwari SN, Prasad R. On ROs-spaces. Portugal Math 1975;34:213-17.
  10. Maji PK, Biswas R, Roy PR. Fuzzy soft sets. J Fuzzy Math 2009;9:589-602.
  11. Ogata H Operations on Topological Spaces and Associated Topology. Math Japonila 1991;36(1):175-184.
  12. Okelo NB. On characterization of various finite subgroups of Abelian groups, Int J Mod Comput Info and Commun Technol 2018;1(5):93-8.
  13. Okelo NB. Theoretical Analysis of Mixed-effects Models with minimized Measurement Error. Int J Math Soft Comp 2018;8(1):55-67.
  14. Okelo NB. Certain properties of Hilbert space operators. Int J Mod Sci Technol 2018;3(6):126-32.
  15. Okelo NB. Certain Aspects of Normal Classes of Hilbert Space Operators, Int J Mod Sci Technol 2018;3(10):203-7.
  16. Okelo NB. Characterization of Numbers using Methods of Staircase and Modified Detachment of Coefficients. Int J Mod Comp Info and Com Technol 2018;1(4):88-92.
  17. Okelo NB. On Characterization of Various Finite Subgroups of Abelian Groups. Int J Mod Comput Info and Commun Technol 2018;1(5):93-8.
  18. Okelo NB. On Normal Intersection Conjugacy Functions in Finite Groups. Int J Mod Comput Info and Commun Technol 2018; 1(6): 111-115.
  19. Okwany I, Odongo D, and Okelo NB. Characterizations of Finite Semigroups of Multiple Operators. Int J Mod Comput Info and Commun Technol 2018;1(6):116-20.
  20. Ramesh R, Mariappan R. Generalized open sets in Hereditary Generalized Topological Spaces J Math Comput Sci 2015;5(2):149-59.
  21. Saha S. Local connectedness in fuzzy setting. Simon Stevin 1987;61:3-13. 
  22. Sanjay M. On α-τ-Disconnectedness and α-τ-connectedness in Topological spaces. Acta Scientiarum Technol 2015;37:395-9.
  23. Shabir M, Naz M. On soft topological spaces. Comput Math Appl 2011;61:1786-99.
  24. Vijayabalaji S, Sathiyaseelan N. IntervalValued Product Fuzzy Soft Matrices and its Application in Decision Making. Int J Mod Sci Technol 2016;1(7):159-63.
  25. Wanjara AO, Okelo NB, Ongati O. On Characterization of Very Rotund Banach Spaces. Int J Mod Comput Info and Commun Technol 2018;1(5):99-102.