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Year 2019, Volume: 8 Issue: 1, 14 - 25, 15.12.2019

Abstract

References

  • M.E. Abd. El.Monsef, E.F. Lashien and A.A Nasef, On I-open sets and I-continuous functionsKyungpook. Math. J, 32 21-30 (1992).
  • A. Acikgoz, S. Yuksel and T. Noiri, α -I-preirresolute functions and β-I-preirresolute functions, Bulletin of the Malaysian Mathematical Sciences and society, 2(28)(1) 01-08 (2005).
  • S.P. Arya and T.M. Nour, Characterization of s-normal spaces, Indian J.Pure. Appl. Math., 21(8), 717-719 (1990).
  • S.G. Crossely and S.K. Hildebrand, Semi topological properties, Fund. Math, 74 233-254 (1972).
  • J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, Math. GN/9901017, (1999) (Internet).
  • H.R. Hamlett and D. Jancovic , Ideal in general topology, Lecture Notes in Pure and Appl. Math, 115-125 (1988).
  • E. Hatir and T. Noiri, On decomposition of continuity via Idealization, Acta Math. Hungar, 96 (4) 341-349 (2002).
  • E. Hatir and T. Noiri, On Hausdroff spaces via ideals and semi I-irresolute functions, European Journal of pure and Applied Mathematics, 2(2) 172-181 (2009).
  • V. Inthumathi, M. ParveenBanu and R. Abinprakash, Decomposition of nano α I-open sets in nano ideal topological spaces, Journal of Physics Conference Series 1139:012086 DOI:10.1088/1742-6596/1139/1/012086 (2018).
  • D. Jancovic and T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97, 295-310 (1990).
  • M. Lellis Thivagar and Carmel Richard, On Nano Forms of Weakly Open Sets, International Journal of Mathematics and Statistics Invention, 1(1), 31-37 (2013).
  • M. Lellis Thivagar and Carmel Richard, On Nano Continuity, Mathematical Theory and Modelling, 3 (7) 32-37 (2013).
  • M. Lellis Thivagar and V. Sutha Devi, New sort of operator in nano ideal topology, Ultra Scientist, 28(1)A 51-64 (2016).
  • M. Lellis Thivagar, Saeid Jafari and V. Sutha Devi, On New class of Contra Continuity in Nano Topology, Italian Journal of Pure and Appl. Math., (2017).
  • M. Lellis Thivagar, Saeid Jafari and Carmel Richard, Remarks on weak form of nano continuity, (communicate), (2015).
  • N. Levine, Semi-open sets, semi-continuity in topological spaces, Amer. Math. Monthly, 70(1) 36-41 (1963).
  • A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deep, On pre continuous and weak pre continuous mappings, Proc.Math.Phys.Soc. Egypt, 53 47-53 (1982).
  • A.S. Mashhour, I.A. Hasanein and S.N. El.Deep, -continuous and -open mappings, Acta. Math. hunger, 41 213-218(1983).
  • T. Noiri, M. Rajamani, V. Inthumathi, On decomposition of g-continuity via idealization, Bull. Cal.Math.Soc, 99 (4) 415-424 (2007).
  • M. Parimala and S. Jafari, On Some New notions in nano ideal topological spaces, International Balkan Journal of mathematics, 1 (3) 85-92 (2018).
  • P. Sathishmohan, V. Rajendran, A. Devika and R. Vani, On nano semi continuity and nano pre continuity, International Journal of Applied Research, 3(2) 76-79 (2017).

Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces

Year 2019, Volume: 8 Issue: 1, 14 - 25, 15.12.2019

Abstract

The aim of this paper is to define and study certain new classes of continuous and irresolute mappings namely nano α-I-continuous, nano semi I-continuous, nano pre I-continuous, nano α-I-irresolute, nano semi I-irresolute and nano pre I-irresolute mappings in nano ideal topological spaces and we discuss some of its properties. Finally, we obtain a decomposition of nano α-I-continuous mapping.

References

  • M.E. Abd. El.Monsef, E.F. Lashien and A.A Nasef, On I-open sets and I-continuous functionsKyungpook. Math. J, 32 21-30 (1992).
  • A. Acikgoz, S. Yuksel and T. Noiri, α -I-preirresolute functions and β-I-preirresolute functions, Bulletin of the Malaysian Mathematical Sciences and society, 2(28)(1) 01-08 (2005).
  • S.P. Arya and T.M. Nour, Characterization of s-normal spaces, Indian J.Pure. Appl. Math., 21(8), 717-719 (1990).
  • S.G. Crossely and S.K. Hildebrand, Semi topological properties, Fund. Math, 74 233-254 (1972).
  • J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, Math. GN/9901017, (1999) (Internet).
  • H.R. Hamlett and D. Jancovic , Ideal in general topology, Lecture Notes in Pure and Appl. Math, 115-125 (1988).
  • E. Hatir and T. Noiri, On decomposition of continuity via Idealization, Acta Math. Hungar, 96 (4) 341-349 (2002).
  • E. Hatir and T. Noiri, On Hausdroff spaces via ideals and semi I-irresolute functions, European Journal of pure and Applied Mathematics, 2(2) 172-181 (2009).
  • V. Inthumathi, M. ParveenBanu and R. Abinprakash, Decomposition of nano α I-open sets in nano ideal topological spaces, Journal of Physics Conference Series 1139:012086 DOI:10.1088/1742-6596/1139/1/012086 (2018).
  • D. Jancovic and T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97, 295-310 (1990).
  • M. Lellis Thivagar and Carmel Richard, On Nano Forms of Weakly Open Sets, International Journal of Mathematics and Statistics Invention, 1(1), 31-37 (2013).
  • M. Lellis Thivagar and Carmel Richard, On Nano Continuity, Mathematical Theory and Modelling, 3 (7) 32-37 (2013).
  • M. Lellis Thivagar and V. Sutha Devi, New sort of operator in nano ideal topology, Ultra Scientist, 28(1)A 51-64 (2016).
  • M. Lellis Thivagar, Saeid Jafari and V. Sutha Devi, On New class of Contra Continuity in Nano Topology, Italian Journal of Pure and Appl. Math., (2017).
  • M. Lellis Thivagar, Saeid Jafari and Carmel Richard, Remarks on weak form of nano continuity, (communicate), (2015).
  • N. Levine, Semi-open sets, semi-continuity in topological spaces, Amer. Math. Monthly, 70(1) 36-41 (1963).
  • A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deep, On pre continuous and weak pre continuous mappings, Proc.Math.Phys.Soc. Egypt, 53 47-53 (1982).
  • A.S. Mashhour, I.A. Hasanein and S.N. El.Deep, -continuous and -open mappings, Acta. Math. hunger, 41 213-218(1983).
  • T. Noiri, M. Rajamani, V. Inthumathi, On decomposition of g-continuity via idealization, Bull. Cal.Math.Soc, 99 (4) 415-424 (2007).
  • M. Parimala and S. Jafari, On Some New notions in nano ideal topological spaces, International Balkan Journal of mathematics, 1 (3) 85-92 (2018).
  • P. Sathishmohan, V. Rajendran, A. Devika and R. Vani, On nano semi continuity and nano pre continuity, International Journal of Applied Research, 3(2) 76-79 (2017).
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İnthumathi Velusamy

Abinprakash Ramalingum This is me

Parveen Banu Muhammed Jaffer This is me

Publication Date December 15, 2019
Published in Issue Year 2019 Volume: 8 Issue: 1

Cite

APA Velusamy, İ., Ramalingum, A., & Muhammed Jaffer, P. B. (2019). Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces. Journal of New Results in Science, 8(1), 14-25.
AMA Velusamy İ, Ramalingum A, Muhammed Jaffer PB. Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces. JNRS. December 2019;8(1):14-25.
Chicago Velusamy, İnthumathi, Abinprakash Ramalingum, and Parveen Banu Muhammed Jaffer. “Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces”. Journal of New Results in Science 8, no. 1 (December 2019): 14-25.
EndNote Velusamy İ, Ramalingum A, Muhammed Jaffer PB (December 1, 2019) Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces. Journal of New Results in Science 8 1 14–25.
IEEE İ. Velusamy, A. Ramalingum, and P. B. Muhammed Jaffer, “Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces”, JNRS, vol. 8, no. 1, pp. 14–25, 2019.
ISNAD Velusamy, İnthumathi et al. “Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces”. Journal of New Results in Science 8/1 (December 2019), 14-25.
JAMA Velusamy İ, Ramalingum A, Muhammed Jaffer PB. Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces. JNRS. 2019;8:14–25.
MLA Velusamy, İnthumathi et al. “Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces”. Journal of New Results in Science, vol. 8, no. 1, 2019, pp. 14-25.
Vancouver Velusamy İ, Ramalingum A, Muhammed Jaffer PB. Some Weaker Forms of Continuous and Irresolute Mappings in Nano Ideal Topological Spaces. JNRS. 2019;8(1):14-25.


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