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

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.

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  • 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).
Journal of New Results in Science-Cover
  • ISSN: 1304-7981
  • Yayın Aralığı: Yılda 3 Sayı
  • Başlangıç: 2012
  • Yayıncı: Tokat Gaziosmanpaşa Üniversitesi