CFP last date
20 May 2024
Reseach Article

A Study on (i,j)g*ssI Closed and Open Sets in Bitopological Spaces

Published on June 2013 by K.indirani, G.sindhu
International Conference on Innovation in Communication, Information and Computing 2013
Foundation of Computer Science USA
ICICIC2013 - Number 3
June 2013
Authors: K.indirani, G.sindhu
51a932e3-c2f0-4621-84bd-00a8822755b1

K.indirani, G.sindhu . A Study on (i,j)g*ssI Closed and Open Sets in Bitopological Spaces. International Conference on Innovation in Communication, Information and Computing 2013. ICICIC2013, 3 (June 2013), 32-35.

@article{
author = { K.indirani, G.sindhu },
title = { A Study on (i,j)g*ssI Closed and Open Sets in Bitopological Spaces },
journal = { International Conference on Innovation in Communication, Information and Computing 2013 },
issue_date = { June 2013 },
volume = { ICICIC2013 },
number = { 3 },
month = { June },
year = { 2013 },
issn = 0975-8887,
pages = { 32-35 },
numpages = 4,
url = { /proceedings/icicic2013/number3/12277-0158/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 International Conference on Innovation in Communication, Information and Computing 2013
%A K.indirani
%A G.sindhu
%T A Study on (i,j)g*ssI Closed and Open Sets in Bitopological Spaces
%J International Conference on Innovation in Communication, Information and Computing 2013
%@ 0975-8887
%V ICICIC2013
%N 3
%P 32-35
%D 2013
%I International Journal of Computer Applications
Abstract

An Ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. In this paper, (i,j)g*ss closed and open sets are introduced with respect to an ideal in a bitopological space and their properties are investigated. Additionally, we compare them with other sets to show their relationships and characterize many other results.

References
  1. A. Pushpalatha and K. Anitha , g*s-Closed sets in topological spaces, Int. J. Contemp. Math. Sciences, Vol. 6,2011,no. 19, 917-929.
  2. A. Pushpalatha, Studies on Generalizations of Mappings in Topological spaces, Ph. D Thesis,
  3. Andrijevic D(1986) Semi-pre-open sets. Mat Vesnik 38:24-32
  4. Definition Bank in General Topology by G. B. Navalagi.
  5. Dontchev J(1995) On generalizing semi- pre-open sets. Mem. Fac. Sci. Kochi Univ. Ser. A. Math. , 16,35-48
  6. Generalised closed sets with respect to an Ideal in Bitopological spaces. T. Noiri and
  7. H. Maki, R. Devi and K. Balachandran , Associated Topologies of Generalized ?-closed sets and ?- Generalized closed sets, Mem. Sci. Kochi Univ. Ser. A. Math. 15(1994),51-63.
  8. J. C. Kelly, Bitopological spaces. Proc. London Math. Soc. 13(1963). 71-89.
  9. K. Chandrasekhara Rao and K. Kannan, Regular generalized star closed sets in bitopological spaces, Thai Journal of Mathematics, Vol 4, (2) (2006), 341–349.
  10. K. Indirani,V. Rajendran and P. Sathishmohan, On wg?-I-continuity and w?g-I-continuity, Global Journal of Advances in Pure and Applied Mathematics Volume 1. Issue 1(2012),1-8.
  11. K. Indirani and H. Jude Immaculate. ( i,j)g*?s closed and (i,j)g*ss closed sets in Bitopological Spaces-M. Phil Thesis(2013)
  12. Kuratowski. K. Topology,Vol I, Academic Press(New York,1966)
  13. M. Lellis Thivagar and Nirmala Mariappan- On Weak Separation Axioms Associated with (1, 2)?-Sg-Closed Sets-Int. Journal of Math. Analysis, Vol. 4, 2010, no. 13, 631 - 644
  14. Levine. N(1963)Semi-open sets and semi continuity in topological spaces. Amer. Math. Monthly 70:36-41
  15. M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hunger, 119(4) (2008), 365 – 371.
  16. M. Rajamani and V. Rajendran, A study on g?-closed sets in ideal topological spaces,M. Phil. , Thesis (2009).
  17. M. Sheik John and P. Sundaram,g*Closed sets in Bitopological spaces.
  18. M. Sheik John and K. Balachandran , Semi-generalized continuous maps and semi-spaces,Bull. Fukuoka Univ. Ed. Part III,40(1991),33-40
  19. Mashhour AS,M. E Abd El-Monsef and SN El Deeb(1982) On precontinuos and weak Precontinuous functions. Proc. Math. Phys. Soc. Egypt 53:47-53
  20. N. Levine , Generalized closed sets in Topology, Rend. Circ. Mat. Palermo 19(1970),89-96.
  21. Njastad O(1965) On some classes of nearly open sets. Pacific. J. Math. 15:961-970
  22. O. A. El-Tantawy and H. M. Abu-Donia, Generalized Separation Axioms in Bitopological Spaces, The Arabian Jl for Science & Engg. Vol. 30, No. 1A (2005), 117-129.
  23. O. A. El-Tantawy* and H. M. Abu-Donia-Generalized Separation axioms in Bitopological spaces- 2005 The Arabian Jl for Science and Engineering, Volume 30, Number 1A.
  24. O. Ravi, S. Ganesan, S. Tharmar and R. G. Balamurugan – Minimal g-closed sets with respect to an Ideal-Int. J. Adv. Pure and Applied Math. Vol I(2011) 1-12.
  25. P. Bhattacharya and B. K. Lahari , Semi- Generalized closed sets in Topology,Indian J. Math,29(3),pp. 375- 382(1987).
  26. Palaniappan N and KC Rao(1993) Regular generalized closed sets. Kyungpook. Math. J 33:211-219
  27. R. Devi, H. Maki and K. Balachandran, Semi-Generalized closed maps and Generalized closed maps, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. , 14 (1993),41-54
  28. R. Devi,K. Balachandran and H. Maki , Generalized ?- closed maps and ?-Generalized closed maps,Indian J. Pure. Appl. Math. ,29(1)(1998),37-49.
  29. S. P. Arya and T. Nour ,Characterizations of S-normal Spaces , Indian J. pure Appl. Math. , 21, pp. 717- 719(1990).
  30. Stone M –Application of the theoryof Boolean rings to general topology. Trans. Amer. Math. Soc 41:374-491
  31. T. Fukutake. On generalized closed sets in Bitopological spaces. Bull, Fukuoka Univ , Ed. III. 35(1985). 19-28.
  32. Vaidyanathasamy. R. The Localization theory in set topology,Proc,Indian Acad Sci, Sect A. 20(1945)51-61
Index Terms

Computer Science
Information Sciences

Keywords

(i j)g*ss Closed Sets (i j)g*ssi Closed Sets And (i j)g*ssi Open Sets