Volume 8 | Number 2 | Year 2014 | Article Id. IJMTT-V8P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V8P517
The purpose of this paper is to introduce strongly πgrirresolute functions, strongly regular πgr-irresolute functions and strongly β- πgr-irresolute functions and study some of their basic properties. Also, some new forms of homeomorphism are defined and obtained their characterizations.
[1] M.E.Abd, EI. Monsef, S.N.EL.Deeb and R.A. Mashmoud, “β-open sets and β-continuous mappings”, Bull. Fac. Sci. Asiut Univ.,12(1983), 77-90.
[2] S.P.Arya and R.Gupta, “On strongly continuous mappings”, Kyungpook Math,13(1974),131-143.
[3] D.A.Carnahan,“Some properties related to compactness in topological spaces”, Ph.D,Thesis, Univ. of Arkansas, (1973).
[4] J.Dontchev, “ The characterization of spaces and maps via semi-preopen sets”, Indian J.Pure Appl Math., 25 (1994), 939-947.
[5]J.Dontchev, On submaximal Spaces, Tamkang J.Math., 26(1995),253-260.
[6] J.Dontchev, T.Noiri, “Quasi normal spaces and πg-closed sets”, Acta Math. Hungar , 89 (3) ,2000,211- 219.
[7] Janaki.C, “ Studies on πgα-closed sets in topology”, Ph.D. Thesis, Bharathiar University, Sep- 2009.
[8] Jeyanthi.V and Janaki.C, “gr-closed sets in topological spaces “,Asian Journal of Current Engg. and Maths 1:5 sep 2012, 241-246.
[9]Jeyanthi.V and janaki.C ,“ On πgr-continuous functions in topological spaces”,IJERA,Vol 1, issue 3, Jan-Feb- 2013.
[10]N. Levine, “Generalized closed sets in topology, Rend. Cir. Mat. Palermo, 19(1970), 89-96.
[11] N.Levine, “Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70(1963), 36-41.
[12] R.A. Mahmood and M.E.Abd El.Monsef, “β-irresolute and β-topological invariant”,Proc. Pakistan Acad. Sci., 27(1990),285-296.
[13] H.Maki, P.Sundaram and K.Balachandran, “On generalized homeomorphisms in topological Spaces”, Bull. Fukuoka Univ.Ed.Part III, 40 (1991), 13-21.
[14] A.S.Mashour, I.A.Hasanein and S.N.EI.Deeb, “A note on semi-continuity and pre- Continuity”, Indian. J .Pure Appl. Math., 13(1982),213-218.
[15] B.M .Munshi and D.S.Bassan, “Super continuous functions”, Indian, J.Pure and Appl.Math., 13(1982), 229-236.
[16] T.Neubrunn, “On Semi-homeomorphisms and related mappings”, Acta Fac. Rerum Natur, Univ. Comenian Math., 33(1977),133-137.
[17] T.Noiri, “Strong forms of continuity in topological spaces”, Rend. Circ.Mat.Palermo (supplement) Ser.II, 12(1986),107-113.
[18]Palaniappan .N and Rao.K.C, “Regular generalized closed sets” , Kyungpook Math .J.33(1993), 211-219.
[19]I.L.Reily and M.K.Vamanamurthy, “On super continuous mappings”,Indian J.Pure appl. Math.,14(1983), 767-772.
[20] L.A.Steen and J.A. Seeback Jr., “Counter examples in topology”, Springer -verlag, NewYork, 1978.
[21] V.Zaitsav, “On certain classes of topological spaces and their bicompactifications”, Dokl Akad Nauk , SSSR (178), 778-779.
[22] I.Zorlutana , T.Noiri and M.Kucuk, “On strongly pre- continuous functions”, Bull. Malays. Math. Sci. Soc., 31(2008), 185-192.
C.Janaki, V.Jeyanthi, "On Strongly πgr-Irresolute Functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 8, no. 2, pp. 129-135, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V8P517