On rgw⍺-Continuous and rgw⍺-Irresolute Maps in Topological Spaces

R. S. Wali; Vijayalaxmi R.Patil

doi:https://doi.org/10.14445/22315373/IJMTT-V45P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 45 | Number 1 | Year 2017 | Article Id. IJMTT-V45P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V45P501

On rgw⍺-Continuous and rgw⍺-Irresolute Maps in Topological Spaces

R. S. Wali, Vijayalaxmi R.Patil

Abstract

The aim of this paper is to introduce a new type of functions called the rgw⍺- continuous map, rgw⍺- irresolute maps, strongly rgw⍺-continuous maps, perfectly rgw⍺-continuous maps and study some of these properties.

Keywords

rgw⍺-open sets, rgw⍺-closed sets, rgw⍺- continuous map, rgw⍺-irresolute maps, strongly rgw⍺- continuous maps, perfectly rgw⍺-continuous.

References

[1] A. S. Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
[2] A.Vadivel & K.vairamamanickam, rgα-Closed sets& rgα-open sets in Topological Spaces, Int J of math ,Analysis Vol 3 , (2009)37,1803-1819.
[3] Al-Omari A and M.S.M.Naorami, On generalized b-closed sets, Bull. Malays. Math. Sci.Soc(2), 32(2009), 19-30.
[4] Arockiarani. I, Balachandran.K and Dontchev J, Some Characterization of gp-irresolute and gp-continuous maps between topological spaces, Mem.Fac.Sci.Kochi Univ.Ser.A Math.,20(1999),93-104.
[5] Balachandran.K, Sundaram.P and Maki.H, On generalized Continuous maps in topological spaces, Mem Fac.Sci.Kochi Univ.Ser.A.Math ., 12(1991),5-13.
[6] Crossley S. G and Hildebrand S.K, Semi Topological properties, Fund.Math.,74(1972),233-254.
[7] D. Andrijevic, Semi-preopen sets, Mat. Vesnik., 38(1)(1986), 24- 32.
[8] D. E. Cameron , Properties of s-closed spaces, prac Amer Math, soc 72(1978),581-586.
[9] Devi R, Balachandran.K and Maki H, On generalized ⍺- continuous maps and ⍺- generalized continuous maps, Far East J. Math. Sci., Special volume (1997), Part I, 1-15.
[10] Devi R, Balachandran.K and Maki H, Semi generalized homeomorphisms and generalized Semi homeomorphisms on topological spaces, Indian J. Pure Appl. Math., 26(1995), 271- 284.
[11] Gnanambal.Y, Balachandran.K, On gpr-continuous functions in topological spaces, Indian J.Pure Appl.Math 1999, 30(6):581- 93.
[12] H. Maki, J. Umehara andT. Noiri,Every Topological space is pre T½ mem Fac sci,Kochi univ,Math ,17 1996,33-42.
[13] H. Maki, R. Devi and K.Balachandran, Associated topologies of generalized α- closed sets and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser.A. Math., 15(1994), 51-63.
[14] J Dontchev , Contra continuous functions and strongly S-closed spaces, Int.J.Math.Sci,19(1996), 15-31.
[15] M. Stone, Application of the theory of Boolean rings to general topology, Trans.Amer. Math.Soc.41(1937),374-481.
[16] Mashhour.A.S., Abd El-Monsef .M.E. and El-Deeb.S.N.On pre continuous mappings and week pre-continuous mappings, Proc Math, Phys.Soc.Egypt 53(1982),47-53.
[17] Munshi B.M. and Bassan D S, g-continuous mappings, Vidya J.Gujarat Univ. B.Sci.,24(1981),63-68.
[18] N .Levine, Generalized closed sets in topology, Rend. Circ Mat. Palermo,19(2) (1970), 89-96.
[19] N .Levine, Semi-open sets and semi-continuity in topological spaces, 70(1963), 36- 41.
[20] N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 1999.
[21] O. N. Jastad, On some classes of nearly open sets, Pacific J. Math., 15(1965),961- 970.
[22] P. Sundaram and M. Sheik John, On w-closed sets in topology, Acta Ciencia Indica 4 (2000) , 389–39.
[23] R.S. Wali and Vijayalaxmi R.Patil, On rgw⍺-closed sets in topological spaces. Int.J. comp. and Math.Sci. Vol 8,(3). 62-70 (2017).
[24] S. Bhattacharya, on generalized regular closed sets, Int J.Contemp .Math science Vol.6 ,201,145-152.
[25] S. Mishra ,et , all , On regular generalized weakly (rgw)closed sets in topological spaces , Int . J. of Math Analysis Vol 6, 2012 no.(30) , 1939-1952.
[26]S.P.Arya and R. Gupta, on stongly continuous functions, Kyungpook Math.j.14:131:143, 1974.
[27] S. P.Arya and T.M. Nour , Chatcterizationsof s-normal spaces, Indian J. Pure Appl, Math 21(1990), 717-719.
[28] S.S. Benchelli, P.G,Patil and Pallavi S. Mirajakar g star w - closed sets in topological spaces. Jl. New results in sciences,Vol. 9, (2015), 37- 45.
[29] S.S. Benchelli, P.G.Patil and P.M.Nalwad, gw -closed sets in topological spaces. Journal of New results in Sci.vol.7, (2014), 7-19.
[30] S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-Closed sets in Topological Spaces, The Global. J. Appl. Math. and Math. Sci,. 2, 2009, 53-63.
[31] S. S. Benchalli and R.S Wali on rω- Closed sets is Topological Spaces, Bull, Malays, Math, sci, soc30 (2007), 99-110.
[32] Veerakumar M.K.R.S., Semi-pregeneralized closed sets, Mem.Fac.Sci.Kochi Univ. Ser. A Math..,.19(1999),33-46.
[33] Y. Gnanambal, On generalized pre regular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28(3)(1997), 351-360.
[34] Yasuf Becerem, On strongly ⍺-continuous functions far east J.Math.Sci. 1:5 0 2000.

Citation :

R. S. Wali, Vijayalaxmi R.Patil, "On rgw⍺-Continuous and rgw⍺-Irresolute Maps in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 45, no. 1, pp. 1-10, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V45P501