Bδg-Homeomorphisms

Year 2018, Issue: 25, 50 - 58, 06.10.2018

Jeyasingh Juliet Jeyapackiam Alwyn Asir

Abstract

In this paper we introduce two new classes of mappings called Bδg-homeomorphism and Bδgc-homeomorphism which are defined using Bδg-closed sets and study their basic properties. We also investigate its group structure of their subgroups. We also investigate its relationship with other types of mappings.

Keywords

Semi-generalized set , semi-homeomorphism mapping , Bδg-homeomorphism mapping , Bδg-closed set

References

• [1] Arya S. P. and Nour T., "Characterizations of S-normal spaces", Indian J. Pure. Appl. Math., 21(8)(1990), 717-719.
• [2] Devi R., Balachandran K. and Maki H., "On generalized-continuous and generalized continuous functions", For East J. Math Sci. Special Volume, Part I (1997), 1-15.
• [3] Dontchev J., "Contra-continuous functions and strongly S-closed spaces", International J. Math. Sci. 19 (1996), 303-310.
• [4] Dontchev J. and Ganster M., "On -generalized closed sets and T3=4-spaces", Mem. Fac. Sci. Kochi Univ. Ser. A, Math., 17 (1996), 15-31.
• [5] Dontchev J, Noiri T, "Contra-semi-continuous functions", Math. Pannonica 10 (1999), 159-168.
• [6] Ganster M., Reilly I. L., "Locally closed sets and alc-continuous functions", Internat. J. Math. Sci. 3 (1989), 417-424.
• [7] Lellis T. M., Meera D. B. and Hatir E., bg-closed sets in Topological spaces", Gem. Math. Notes, Vol 1, No.2, (2010), 17-25.
• [8] Lellis T. M., Meera D. B., "Some new class of generalised continuous functions "Proceedings of the ICMCS2011, 431-434.
• [9] Lellis T. M., Meera D. B., "Notes On Homeomorphisms Via bg-Sets." Journal of Advanced Studies in Topology, Vol.2, No.1 (2011), 34-40.
• [10] Lellis T. M., Meera D. B., "Notes on contra via bg-continuous functions", Bol. Soc. Paran. Mat Vol. 30 No.2, (2012), 109-116.
• [11] Levine N., "Semi-open sets and semi-continuity in topological spaces", Amer. Math. Monthly, 70 (1963), 36-41.
• [12] Levine N., "Generalized closed sets in Topology", Rend. Circ. Math. Palermo, 19 (2) (1970), 89-96.
• [13] Maki H., Devi R. and Balachandran K., "Associated topologies of generalized -closed sets and ®-generalized closed sets", Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 15 (1994), 57-63.
• [14] Mashhour, A. S., Abd El-Monsef, M. E. and El-Debb. S. N., "On precontinuous and weak precontinuous mappings", Proc. Math. and Phys. Soc. Egypt 55 (1982), 47-53.
• [15] Malghan S. R., "Generalized closed maps", J. Karnatak Univ. Sci., 27(1982), 82-88.
• [16] Meera D. B., "Investigation of some new class of weak open sets in general Topology" PhD Thesis, Madurai Kamaraj University, Madurai (2012).
• [17] Munkres J. R., "Topology, A first course", Fourteenth Indian Reprint.
• [18] Njastad O., "On some classes of nearly open sets", Pacific. J. Math. 15(1965), 961-970.
• [19] Noiri T., "Super-continuity and some strong forms of continuity ", Indian J. Pure. Appl Math., 15 (1984), 241-150.
• [20] Noiri T., "On continuous functions", J. Korean Math. Soc. 18 (1980), 161-166.
• [21] Ravi O., Lellis T. M., Balakrishnan M., "Quotient functions related Ekici's a-open sets", Antarctica Journal of Mathematics, 7 (1) (2010), 111-121.
• [22] Starum R., "The algebra of bounded continuous functions into a nonarchime-dianeld", Paci¯c J. Math, 50(1974), 169-185.
• [23] Tong J., "On Decomposition of continuity in topological spaces", Acta Math. Hungar, 54 (12) (1989), 51-55.
• [24] Veera K. M. K. R. S., "bg-closed sets in topological spaces", Bull. Allah. Math. Soc., 18 (2003), 99-112.
• [25] Velicko N. V., "H-closed topological spaces", Amer. Math. Soc. Transl., 78 (1968), 103-118.