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Year 2018, Volume: 47 Issue: 1, 37 - 45, 01.02.2018

Abstract

References

  • D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32.
  • I. Arockiarani, Studies on generalizations of generalized closed sets and maps in topological spaces, Ph.D. Thesis, Bharathiar Univ., Coimbatore, 1997.
  • G. K. Banerjee, On pairwise almost strongly $\theta$-continuous mappings, Bull. Calcutta Math. Soc. 79(1987), 314-320.
  • S. Bose, Semi open sets, semi-continuity and semi open mappings in bitopological spaces, Bull. Calcutta Math. Soc. 73(1981), 237-246.
  • J. Dontchev and H. Maki, On $\theta$-generalized closed sets, Int. J. Math. Sci. 22(1999), 239-249.
  • O. A. El-Tantawi and H. M. Abu-Donia, Generalized separation axioms in bitopological spaces, Arab. J. Sci. Eng., 1(2005), 117-129.
  • T. Fukutake, On generalized closed sets in bitopological spaces, Bull. Fukuka. Univ. of Educ., 35(1985), 19-28.
  • M. S. John, P. Sundaram, $g^*$-closed sets in bitopological spaces, Indian J. Pure Appl. Math., 35(1) (2004), 71-80.
  • J. C. Kelly, Bitopological spaces, Proc. London. Math. Soc. 13(1963), 71-89.
  • F. H. Khedr, $C\alpha$-continuity in bitopological space, Arab. J. Sci. Eng., 17(1) (1992), 85-89.
  • F. H. Khedr and H. S. Al-Saadi, Generalized semi-closed functions in bitopological spaces, J. Egyptian Math. Soc. 20(2012), 14-19.
  • S. S. Kumar, On a decomposition of pairwise continuity, Bull. Calcutta Math. Soc. 89(1997), 441-446.
  • N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
  • N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(1970), 89-96.
  • A. S. Singal and A. S. Arya, On pairwise almost regular spaces, Glasnik Math. 6(26) (1971), 335-343.
  • M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374-481.

Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces

Year 2018, Volume: 47 Issue: 1, 37 - 45, 01.02.2018

Abstract

This paper introduces with a new class of sets called $ij$-strongly $g^*$-closed. We prove that this lies between the class of $\tau_j$-closed sets and the class of $ij$-$g^*$-closed sets. Also we find some basic properties and applications of $ij$-strongly $g^*$-closed sets. We also introduce and study a new class of spaces, namely $ij$-$ST^*_{\dfrac{1}{2}}$ spaces.

References

  • D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32.
  • I. Arockiarani, Studies on generalizations of generalized closed sets and maps in topological spaces, Ph.D. Thesis, Bharathiar Univ., Coimbatore, 1997.
  • G. K. Banerjee, On pairwise almost strongly $\theta$-continuous mappings, Bull. Calcutta Math. Soc. 79(1987), 314-320.
  • S. Bose, Semi open sets, semi-continuity and semi open mappings in bitopological spaces, Bull. Calcutta Math. Soc. 73(1981), 237-246.
  • J. Dontchev and H. Maki, On $\theta$-generalized closed sets, Int. J. Math. Sci. 22(1999), 239-249.
  • O. A. El-Tantawi and H. M. Abu-Donia, Generalized separation axioms in bitopological spaces, Arab. J. Sci. Eng., 1(2005), 117-129.
  • T. Fukutake, On generalized closed sets in bitopological spaces, Bull. Fukuka. Univ. of Educ., 35(1985), 19-28.
  • M. S. John, P. Sundaram, $g^*$-closed sets in bitopological spaces, Indian J. Pure Appl. Math., 35(1) (2004), 71-80.
  • J. C. Kelly, Bitopological spaces, Proc. London. Math. Soc. 13(1963), 71-89.
  • F. H. Khedr, $C\alpha$-continuity in bitopological space, Arab. J. Sci. Eng., 17(1) (1992), 85-89.
  • F. H. Khedr and H. S. Al-Saadi, Generalized semi-closed functions in bitopological spaces, J. Egyptian Math. Soc. 20(2012), 14-19.
  • S. S. Kumar, On a decomposition of pairwise continuity, Bull. Calcutta Math. Soc. 89(1997), 441-446.
  • N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
  • N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(1970), 89-96.
  • A. S. Singal and A. S. Arya, On pairwise almost regular spaces, Glasnik Math. 6(26) (1971), 335-343.
  • M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374-481.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

H. S. Al-saadi

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 1

Cite

APA Al-saadi, H. S. (2018). Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces. Hacettepe Journal of Mathematics and Statistics, 47(1), 37-45.
AMA Al-saadi HS. Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces. Hacettepe Journal of Mathematics and Statistics. February 2018;47(1):37-45.
Chicago Al-saadi, H. S. “Strongly $g^*$-Closed Sets and Strongly $T^*_{\frac{1}{2}}$ Spaces in Bitopological Spaces”. Hacettepe Journal of Mathematics and Statistics 47, no. 1 (February 2018): 37-45.
EndNote Al-saadi HS (February 1, 2018) Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces. Hacettepe Journal of Mathematics and Statistics 47 1 37–45.
IEEE H. S. Al-saadi, “Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 37–45, 2018.
ISNAD Al-saadi, H. S. “Strongly $g^*$-Closed Sets and Strongly $T^*_{\frac{1}{2}}$ Spaces in Bitopological Spaces”. Hacettepe Journal of Mathematics and Statistics 47/1 (February 2018), 37-45.
JAMA Al-saadi HS. Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces. Hacettepe Journal of Mathematics and Statistics. 2018;47:37–45.
MLA Al-saadi, H. S. “Strongly $g^*$-Closed Sets and Strongly $T^*_{\frac{1}{2}}$ Spaces in Bitopological Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, 2018, pp. 37-45.
Vancouver Al-saadi HS. Strongly $g^*$-closed sets and Strongly $T^*_{\frac{1}{2}}$ spaces in bitopological spaces. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):37-45.