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I*g-normal and I*g-regular spaces

Year 2014, Volume: 3 Issue: 6, 15 - 26, 01.06.2014

Abstract

I∗g-normal and I∗g-regular spaces are introducedand various characterizations and properties are given. Characterizations of normal, mildly normal, *g-normal and regular spacesare also given

References

  • M. E. Abd EL. Monsef, M. Lellis Thivagar and S. Rosemary, αˆg-closed sets in topological spaces, Assiut Univ. J. of Math and Comp. sci., 36(1)(2007), 43-51.
  • J. Dontchev, M. Ganster and T. Noiri, Unified approach of generalized closed sets via topological ideals, Math. Japonica., 49(1999), 395-401.
  • J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology and its Appli- cations, 93(1999), 1-16.
  • E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205- 2
  • D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), no. 4, 295-310.
  • K. Kuratowski, Topology, Vol. I, Academic Press (New York, 1966).
  • 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. Mat. Palermo (2), 19(1970), 89-96.
  • S. N. Maheshwari and R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelles, 89(1975), 395-402.
  • H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. III, 42(1993), 13-21.
  • H. Maki, R. Devi and K. Balachandran, Associated topologies of generalized α- closed sets and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Math., 15(1994), 51-63.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53(1982), 47-53.
  • B. M. Munshi, Separation Axioms, Acta Ciencia Indica, 12(1986), 140-144.
  • M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(2008), no. 4, 365-371.
  • O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), no. 3, 961-9
  • T. Noiri and V. Popa, On g-regular spaces and some functions, Mem. Fac. Sci. Kochi Univ. Math., 20(1999), 67-74.
  • T. Noiri, Almost αg-closed functions and separation axioms, Acta Math. Hungar., 82(1999), no.3, 193-205.
  • N. Palaniappan and K. Chandrasekra Rao, Regular generalized closed sets, Kyung- pook Math. J., 33(1993), no. 2, 211-219.
  • O. Ravi, S. Tharmar, M. Sangeetha and J. Antony Rex Rodrigo, *g-closed sets in ideal topological spaces, Jordan Journal of Mathematics and Statistics, 6(1)(2013), 1
  • V. Renuka Devi, D. Sivaraj and T. Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108(2005), no. 3, 197-205.
  • M. Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D, Thesis, Bharathiar University, Coim- batore, (2002).
  • M. K. Singal and A. R. Singal, Mildly normal spaces, Kyungpook Math. J., 13(1973), 27-31.
  • R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1946).
Year 2014, Volume: 3 Issue: 6, 15 - 26, 01.06.2014

Abstract

References

  • M. E. Abd EL. Monsef, M. Lellis Thivagar and S. Rosemary, αˆg-closed sets in topological spaces, Assiut Univ. J. of Math and Comp. sci., 36(1)(2007), 43-51.
  • J. Dontchev, M. Ganster and T. Noiri, Unified approach of generalized closed sets via topological ideals, Math. Japonica., 49(1999), 395-401.
  • J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology and its Appli- cations, 93(1999), 1-16.
  • E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205- 2
  • D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), no. 4, 295-310.
  • K. Kuratowski, Topology, Vol. I, Academic Press (New York, 1966).
  • 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. Mat. Palermo (2), 19(1970), 89-96.
  • S. N. Maheshwari and R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelles, 89(1975), 395-402.
  • H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. III, 42(1993), 13-21.
  • H. Maki, R. Devi and K. Balachandran, Associated topologies of generalized α- closed sets and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Math., 15(1994), 51-63.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53(1982), 47-53.
  • B. M. Munshi, Separation Axioms, Acta Ciencia Indica, 12(1986), 140-144.
  • M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119(2008), no. 4, 365-371.
  • O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), no. 3, 961-9
  • T. Noiri and V. Popa, On g-regular spaces and some functions, Mem. Fac. Sci. Kochi Univ. Math., 20(1999), 67-74.
  • T. Noiri, Almost αg-closed functions and separation axioms, Acta Math. Hungar., 82(1999), no.3, 193-205.
  • N. Palaniappan and K. Chandrasekra Rao, Regular generalized closed sets, Kyung- pook Math. J., 33(1993), no. 2, 211-219.
  • O. Ravi, S. Tharmar, M. Sangeetha and J. Antony Rex Rodrigo, *g-closed sets in ideal topological spaces, Jordan Journal of Mathematics and Statistics, 6(1)(2013), 1
  • V. Renuka Devi, D. Sivaraj and T. Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108(2005), no. 3, 197-205.
  • M. Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D, Thesis, Bharathiar University, Coim- batore, (2002).
  • M. K. Singal and A. R. Singal, Mildly normal spaces, Kyungpook Math. J., 13(1973), 27-31.
  • R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1946).
There are 23 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

O. Ravi This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 3 Issue: 6

Cite

APA Ravi, O. (2014). I*g-normal and I*g-regular spaces. Journal of New Results in Science, 3(6), 15-26.
AMA Ravi O. I*g-normal and I*g-regular spaces. JNRS. June 2014;3(6):15-26.
Chicago Ravi, O. “I*g-Normal and I*g-Regular Spaces”. Journal of New Results in Science 3, no. 6 (June 2014): 15-26.
EndNote Ravi O (June 1, 2014) I*g-normal and I*g-regular spaces. Journal of New Results in Science 3 6 15–26.
IEEE O. Ravi, “I*g-normal and I*g-regular spaces”, JNRS, vol. 3, no. 6, pp. 15–26, 2014.
ISNAD Ravi, O. “I*g-Normal and I*g-Regular Spaces”. Journal of New Results in Science 3/6 (June 2014), 15-26.
JAMA Ravi O. I*g-normal and I*g-regular spaces. JNRS. 2014;3:15–26.
MLA Ravi, O. “I*g-Normal and I*g-Regular Spaces”. Journal of New Results in Science, vol. 3, no. 6, 2014, pp. 15-26.
Vancouver Ravi O. I*g-normal and I*g-regular spaces. JNRS. 2014;3(6):15-26.


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