SOME NEW SEPARATION AXIOMS VIA gr-b-I-OPEN SETS
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Abstract
The purpose this paper is to introduce gr-b-I- open sets, via this
concept we study some weak separation axioms in ideal topological
spaces. The implications of these axioms among themselves and with the
known axioms are investigated
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References
[1] Nagaveni, N. and Narmadha, A. (2012). On regular b-closed sets in topological spaces. In Heber International Conference on Applications of Mathematics and Statistics, HICAM, 5-7 . [2] Nagaveni, A. and Narmadha ,A. (2011). A note on regular b-closed sets in topological spaces. Proc. UGC and DST-Curie sponsored International Conference on Mathematics and its Applications- A New Wave, ICMANW, 21-22. [3] Andrijević, D. (1996). On b-open sets. Matematički Vesnik, 48(205): 59-64.
[4] Levine, N. (1970). Generalized closed sets in topology. Rendiconti del Circolo Matematico di Palermo, 19(1): 89-96.
[5] Palaniappan, N. and Chandrasekhara, K. (1993). Regular generalized closed sets, Kyungpook Mathematics Journal, 33: 211-219. [6] Kuratowski, K. (1966). Topology, Academic Press, New York. [7] Vaidyanathaswamy, R. (1944). The localisation theory in set-topology. In Proceedings of the Indian Academy of Sciences-Section A , 20(1): pp. 51-61). Springer India. [8] Bhattacharya, S. (2011). On generalized regular closed sets. International Journal Contemp. Mathematics Sciences, 6(3): 145-152.
[9] Balaji, R., and Rajesh, N. (2013). Some new separation axioms in ideal topological spaces. International Journal of Engineering, 2(4): 38-48 [10] Velicko, N. V. (1968). H-closed topological spaces. American Mathematical Society, 78(2): 103-118.
[11] Caldas, M., and Jafari, S. (2007). On some applications of b-open sets in topological spaces, Kochi Journal of Mathematics. Japan, 2: 11-79.. [12] Caldas; M., Jafari, S., and Noiri, T. (2006). On Λ b-sets and the associated topologyτ Λ b. Acta Mathematica Hungarica, 110(4): 337-345. . 13. Park, J. H. (2006). Strongly θ-b-continuous functions. Acta Mathematica Hungarica,110(4):347-359.
14. Guler, A. C. and Aslim, G. (2005). b-I-open sets and decomposition of continuity via idealization. Proceedings of Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan, 22: 27-32.
15. Azad, K. K. (1981). On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity. Journal of Mathematical Analysis and Applications, 82(1): 14-32.
[16] alias Sathya, S. and Murugesan, S. (2013). On regular Pre Semi I closed sets in ideal topological spaces. International Journal of Mathematics and soft computing, 3(1): 37-46.
[17] Keskin; A. Noiri, T. and Yüksel, Ş. (2004). Idealization of a decomposition theorem. Acta Mathematica Hungarica, 102(4): 269-278.
[18] Akdağ, M. (2007). On bI-open sets and bI-continuous functions. International Journal of Mathematics and Mathematical Sciences, 2007. [19] Dontchev, J. (1995). On Hausdorff Spaces via Topological Ideals and I-irresolute Functions. Annals of the New York Academy of Sciences, 767(1): 28-38.
[20] Balaji, R. and Rajesh, N. (2014). SOME NEW SEPARATION AXIOMS VIA $ b $-$mathcal {I} $-OPEN SETS. International Journal of Pure and Applied Mathematics, 94(2): 223-232.