Notions of Decomposition of β_G^* -Continuity Via Grills

Main Article Content

Article Sidebar

Published Sep 11, 2021
V. BEULAH Dr. Jessie Theodore Dr.D.Premalatha

Abstract

In this paper, we have introduced betaG*-local function as betaG*,tou(A)={x in X : U intersection A in G for every U in beta open sets(X)}, where the family of semi-preopen sets  betaO(x)={U in betaO(X)  : x in U} in the grill topological space (X, τ, G).   Also, we have investigated the decomposition of betaG*-continuous map in the grill topological space.  Furthermore, the weakly betaG* -continuous map is defined and examined.

How to Cite

V. BEULAH, Dr. Jessie Theodore, & Dr.D.Premalatha. (2021). Notions of Decomposition of β_G^* -Continuity Via Grills. SPAST Abstracts, 1(01). Retrieved from https://spast.org/techrep/article/view/289
Abstract 14 |

Article Details

Keywords

Keywords: β_G^*-local function, grill, β-open set, β_G^* -continuous map.

References
[1] A¸cikg¨oz, A., Noiri, T. and Y¨uksel S¸ A decomposition of continuity in ideal topological spaces, Acta Math. Hungar. 105 (4), 285–289, 2004.
[2] Ahmad Al-Omari and Takashi Noiri, Weakly φ-continuous functions in grill topological spaces, Hacettepe Journal of Mathematics and Statistics Volume 41 (6) (2012), 785 – 793.
[3] D. Andrijevic, Semi-preopen sets, Mat.Vesnik, 38 (1986), 24-32.
[4] Chattopadhyay, K. C., Nj˚astad, K. C. and Thron W. J. Merotopic spaces and extensions of closure spaces, Can. J. Math. 35 (4), 613–629, 1983.
[5] Chattopadhyay, K. C. and Thron, W. J. Extensions of closure spaces, Can. J. Math. 29 (6), 1277–1286, 1977.
[6] Choqet, G. Sur les notions de filter et grill, Comptes Rendus Acad. Sci. Paris 224, 171–173, 1947.
[7] Fomin, S. Extensions of topological spaces, Ann. of Math. 44, 471–480, 1943.
[8] Hatir, E. and Jafari, S, On some new classes of sets and a new decomposition of continuity via grills, J. Ads. Math. Studies. 3 (1), 33–40, 2010.
[9] Jankovi´c, D. and Hamlet, T. R. New topologies from old via ideals, Amer. Math. Monthly 97, 295–310, 1990.
[10] Kuratowski, K. Topology I (Academic Press, New York, 1966).
[11] Levine, N. A decomposition of continuity in topological spaces, Amer Math. Monthly 68, 36–41,
1961.
[12] Levine, N. Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70,
44–46, 1963.
[13] Mashhour, A. S., Abd El-Monsef, M. E. and El-Deeb, S. N. On pre-continuous and weak
pre continuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47–53, 1982.
[14] Renukadevi, V. Relation between ideals and grills, J. Adv. Res. Pure Math. 2 (4), 9–14, 2010.
[15] Rose, D. A. Weak continuity and almost continuity, Internat. J. Math. Math. Sci. 7, 311–
318, 1984.
[16] Roy, B. and Mukherjee, M. N. On a typical topology induced by a grill, Soochow J. Math. 33 (4), 771–786, 2007.
[17] Thron, W. J. Proximity structure and grills, Math. Ann. 206, 35–62, 1973.
[18] Vaidyanathaswamy, R. Set Topology (Chelsea Publishing Company, New York, 1960)
Section
NS3: Mathematics & Statistics