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

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

İnthumathi Velusamy , Abinprakash Ramalingum Parveen Banu Muhammed Jaffer

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.

Keywords

nano pre I-continuous map, nano semi I-continuous map, nano α -I-continuous map, nano I-irresolute map, nano ideal topological spaces

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).