Prabhavati S. Prabhavati S. Mandalageri, Revanasiddappa S. Wali

On αrω-Homeomorphisms in Topological Spaces

A bijection f:(X, τ)→(Y, σ) is called αrω-homeomorphism if f and f−1 are αrω-continuous. Also we introduce new class of maps, namely αrωc-homeomorphisms which form a subclass of αrω-homeomorphisms. This class of maps is closed under composition of maps. We prove that the set of all αrωc-homeomorphisms forms a group under the operation composition of maps.

Keywords:

αrω-closed maps, αrω-closed maps and αrω-open maps, αrω-open maps αrω-homeomorphism, αrωc-homeomorphism,

PDF

___

[1] M E. Abd El-Monsef, S.N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.
[2] D. Andrijevic, Semi-preopen sets, Mat. Vesnik., 38(1) (1986), 24-32.
[3] S P. Arya and R. Gupta, On strongly continuous functions, Kyungpook Math. Jour. 14:131:143, 1974
[4] S. P. Arya and T.M. Nour, Chatcterizationsof s-normal spaces, Indian Jour. Pure Appl, Math 21(1990), 717-719
[5] S. S. Benchalli and R.S Wali, On rw-closed sets is topological spaces, Bull, Malays, Math, sci, soc30 (2007), 99-110
[6] S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-closed sets is topological spaces, The global. Jour. Appl. Math. and Math. Sci,. 2, 2009, 53-63.
[7] S. Bhattacharya, on generalized regular closed sets, Int Jour. Contemp. Math science Vol.6 ,201,145-152
[8] D. E. Cameron , Properties of s-closed spaces, prac Amer Math, soc 72(1978),581-586
[9] R. Devi, K. Balachandran and H. Maki, semi-generalized homeomorphisms and generalized semi homeomorphisms in Topological Spaces , Indian Jour,Closed Maps, J. Karnatk Univ. Sci., 27 (1982), 82-88.
[10] J. Dontchev, Contra continuous functions and strongly S-closed spaces, Int. Jour. Math. Sci, 19 (1996), 15-31.
[11] Y. Gnanambal, On generalized pre regular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28(3)(1997), 351-360.
[12] C. Janaki and Renu Thomas , on R*- Closed sets in Topological Spaces, Int. Jour. of Math Archive 3(8) 2012, 3067-3074
[13] O. N. Jastad, On some classes of nearly open sets, Pacific J. Math., 15(1965),961- 970
[14] A. Jayalakshmi & C.Janaki, on ωgrα-closed sets in Topological Spaces, Int J of maths 3(6) 2012, 2386-2392
[15] V. Joshi, S. Gupta, N. Bhardwaj, R. kumar, on Generalised pre Regular weakly(gprω)-closed set in sets in topological spaces, int. math foruro Vol(7)2012(40)1981-1992
[16] N. Levine, Generalized closed sets in topology, Rend. Circ Mat. Palermo,19(2) (1970), 89-96.
[17] N. Levine, Semi-open sets and semi-continuity in topological spaces, 70(1963), 36- 41.
[18] H. Maki, J. Umehara and T. Noiri, Every Topological space is pre T½ mem Fac sci, Kochi univ, Math ,17 1996,33-42
[19] H. Maki, P. Sundaram and K. Balachandran, On generalized homeomorphisms in topological spaces, Bull. Fukuoka Univ. Ed, part-III, 40(1991), 13-21
[20] 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.
[21] A. S. Mashhour, M.E. Abd El-Monsef and S.N.El-Deeb, On pre-continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
[22] S. Mishra, etc., On regular generalized weakly (rgw) closed sets in topological spaces, Int . Jour. of Math Analysis Vol 6, 2012 no.(30) , 1939-1952
[23] N. Nagaveni, Studies on generalizations of homeomorphisms in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 1999.
[24] A. Pushpalatha, Studies on generalizations of mapping in topological spaces, PhD Thesis, Bharathiar university, Coimbatore ,2000
[25] S. Sakthivel and N.Uma, On wgrα-homeomorphisms in Topological Spaces, Int. Jour. of Math. Trends and Tech. Vol5, Jan 2014 ,10-15
[26] T. Shlya Isac Mary and P.Thangavelv, on Regular pre-semi closed sets in topological spaces , KBM Jour. of Math Sc and comp Applications 2010(1), 9-17
[27] T. Shyla Isac Mary, P. Thangavelu, rps-homeomorphisms in topological spaces, Asian Jour. of Current Engg and Maths 2: 1 Jan –Feb (2013) 74 - 76.
[28] M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41(1937), 374-481.
[29] P. Sundaram and M. Sheik John, On ω-closed sets in topology, Acta Ciencia Indica 4 (2000), 389–39
[30] A.Vadivel and K. Vairamanickam, rgα-homeomorphisms in topological spaces, Int. Jour. of Math. Anal, Vol. 4, 2010, no. 18, 881 –890
[31] A.Vadivel and K. Vairamamanickam, rgα-Closed sets and rgα-open sets in topological spaces, Int. Jour. of math ,Anal Vol 3 , (2009)37,1803-1819
[32] M. K. R. S.Veera Kumar, g*-preclosed sets, Acts Ciencia indica, 28(1), 2002, 51-60.
[33] M. K. R. S. Veera kumar, On α-generalized regular closed sets, Indian Jour. of Math, 44(2) 2002 ,165-181
[34] R. S. Wali and Prabhavati S. Mandalgeri, On α regular ω-open sets in topological spaces, Jour. of comp & Math Sci., Vol 5(6), 2014, 490-499
[35] R. S. Wali and Prabhavati S. Mandalgeri, On αrω-continuous and αrω-Irresolute Maps in Topological Spaces, IOSR–JM, Volume 10, Issue 6 Ver. VI (2014), 14–24
[36] R. S. Wali and Prabhavati S. Mandalgeri, On αrω-closed and αrω-open maps in topological spaces, Int Journal of Applied Research 2015; 1(11), 511–518
[37] R. S. Wali and Prabhavati S Mandalgeri, On α regular ω-closed sets in Topological spaces, Int. J. of Math Archive 5(10), 2014, 68-76.
[38] B. Yasuf, On strongly α-continuous functions, far east Jour. Math. Sci 1(5), 2000

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

Arşiv

On αrω-Homeomorphisms in Topological Spaces

αrω-closed maps, αrω*-closed maps and αrω-open maps, αrω*-open maps αrω-homeomorphism, αrωc-homeomorphism,

___

αrω-closed maps, αrω-closed maps and αrω-open maps, αrω-open maps αrω-homeomorphism, αrωc-homeomorphism,