##plugins.themes.academic_pro.article.main##
Abstract
In this paper, we introduce and study two new of functions called b-δ- continuous function by using the notions of b-δ-open sets and b-δ-closed sets. Â
Keywords: δ - open sets, b-open set, b-δ-open sets, b-δ-closed sets, b-δ-continuous function.##plugins.themes.academic_pro.article.details##
How to Cite
Anuradha, D. S., & Padmanaban, S. (2015). On b-δ-continuous functions. International Journal of Emerging Trends in Science and Technology, 2(07). Retrieved from https://igmpublication.org/ijetst.in/index.php/ijetst/article/view/811
References
1. M.E.Abd El-Monsef, S.N.El-Deeb, R.AMahmoud," -open sets and -continuous mappings," Bull. fac. Sci.Assi. Univ.,(12), pp.77-90, 1983.
2. D. R. Andrew and E. K. Whittlesy, "Closure continuity, " Amer. Math. Month. , (73), pp.758 - 759, 1966.
3. D. Andrijevic, "Semi-preopen sets, " Mat. Vesnik, (18), pp.24 - 32, 1986.
4. D. Andrijevic, "On b-open sets, " Mat. Vesnik, (48), pp.59 - 64, 1996.
5. R.W.Bagley,E.H.Connwll and J.D.McKnight Jr., "on properties characterizing pseudo-compact spaces, " Proc.Amer.Math.Soc.,9, pp.500-506. 1958.
6. D.Carnahan, "Some properties related to compactness in topological spaces, " Ph.D., Thesis, Univ. of Arkansas, 1973.
7. A. Cs´asz´ar, ´ "General Topology, "Adam Higler Ltd, Bristol, 1978.
8. R. David, "Algebraic topology, "2008
9. A.A.El.Atik, "A study of some types of mappings on topological spaces,†M.Sc. Thesis,Faculty of science, Tanta University,Tanta, Egypt, 1997.
10. S.Ganguly and K.Dutta, "Strongly δ -continuous function and topology on function space, " Bull.Stiint. Univ. Buaia Mare, Romania.,(1), pp.39 - 52, 2002.
11. T.Husain, “Almost continuous functions, " Prace Mat., (10), pp.01 - 07, 1996.
12. N. Levine, "A decomposition of continuity in topological spaces," Amer. Math. Month, (68), pp.44 - 46, 1961.
13. N. Levine, "Semi-open sets and semi-continuity in topological spaces, " Amer. Math. Monthly, (70), pp.36 – 41,1963.
14. N. Levine, "Generalized closed sets in topology,†Rend Circ Mat Palermo, (19), pp.89 - 96, 1970.
15. A. S. Mashhour, M. E. Abd El-Monsef, and S.N. El-Deeb, "On precontinuous and weak precontinuous functions, " Proc. Math. Phys. Soc. Egypt, (53),pp. 47 – 53, 1982.
16. A. S. Mashhour,I.A.Hasanein and S.N.El-Deep, " -continuous and -open mappings, " Acta Math. Hungar.,(41), pp.213-218,1982.
17. Klaus Janich, "Topology, Springer, " R(2006).
18. A. A. Nasef, "On b-locally closed sets and related topic, " Chaos, Solitons and Fractals, (12), pp.1909 – 1915,2001.
19. T. Noiri, "Between continuity and weak continuity, " Boll.Un.Mat.Ital(4)9,647-654,1974.
20. T. Noiri, "On δ -Continuous functions, " J.Korean Math Soc., (16), pp.161 - 166, 1980.
21. J.H.Park, "Strongly θ-b-continuous," Acta Math. Hunger.,110(4), pp.347-359, 2006.
22. S.Padmanaban, "On b- δ-open sets in topological spaces," Int Jr. of Mathematical Sciences & Applications,(3), pp.365-371, 2013.
23. J.Porter and J.Thomas, "On H-closed minimal Hausdorff spaces, "Trans.Amer.Math.Soc., 118, 159-170,1974.
24. U.Sengul, "on almost b-continuous functions, " Int. J. Contemp. Math. Sciences, 3(30), pp.1469-1480,2008.
25. M. Stone, "Applications of theory of Boolean rings to general topology,"Trans.Amer. Math. Soc.,(41),pp.375 – 381,1937.
26. N. V. Velicko, "H-closed topological spaces," Amer. Math. Soc. Transl., (78), pp.103 - 118, 1968.
27. I.Zorlutuna, "On b-closed spaces and θ-b-continuous functions, " The Arabian J. sci. eng., (34), pp. 205 – 216,2009.
2. D. R. Andrew and E. K. Whittlesy, "Closure continuity, " Amer. Math. Month. , (73), pp.758 - 759, 1966.
3. D. Andrijevic, "Semi-preopen sets, " Mat. Vesnik, (18), pp.24 - 32, 1986.
4. D. Andrijevic, "On b-open sets, " Mat. Vesnik, (48), pp.59 - 64, 1996.
5. R.W.Bagley,E.H.Connwll and J.D.McKnight Jr., "on properties characterizing pseudo-compact spaces, " Proc.Amer.Math.Soc.,9, pp.500-506. 1958.
6. D.Carnahan, "Some properties related to compactness in topological spaces, " Ph.D., Thesis, Univ. of Arkansas, 1973.
7. A. Cs´asz´ar, ´ "General Topology, "Adam Higler Ltd, Bristol, 1978.
8. R. David, "Algebraic topology, "2008
9. A.A.El.Atik, "A study of some types of mappings on topological spaces,†M.Sc. Thesis,Faculty of science, Tanta University,Tanta, Egypt, 1997.
10. S.Ganguly and K.Dutta, "Strongly δ -continuous function and topology on function space, " Bull.Stiint. Univ. Buaia Mare, Romania.,(1), pp.39 - 52, 2002.
11. T.Husain, “Almost continuous functions, " Prace Mat., (10), pp.01 - 07, 1996.
12. N. Levine, "A decomposition of continuity in topological spaces," Amer. Math. Month, (68), pp.44 - 46, 1961.
13. N. Levine, "Semi-open sets and semi-continuity in topological spaces, " Amer. Math. Monthly, (70), pp.36 – 41,1963.
14. N. Levine, "Generalized closed sets in topology,†Rend Circ Mat Palermo, (19), pp.89 - 96, 1970.
15. A. S. Mashhour, M. E. Abd El-Monsef, and S.N. El-Deeb, "On precontinuous and weak precontinuous functions, " Proc. Math. Phys. Soc. Egypt, (53),pp. 47 – 53, 1982.
16. A. S. Mashhour,I.A.Hasanein and S.N.El-Deep, " -continuous and -open mappings, " Acta Math. Hungar.,(41), pp.213-218,1982.
17. Klaus Janich, "Topology, Springer, " R(2006).
18. A. A. Nasef, "On b-locally closed sets and related topic, " Chaos, Solitons and Fractals, (12), pp.1909 – 1915,2001.
19. T. Noiri, "Between continuity and weak continuity, " Boll.Un.Mat.Ital(4)9,647-654,1974.
20. T. Noiri, "On δ -Continuous functions, " J.Korean Math Soc., (16), pp.161 - 166, 1980.
21. J.H.Park, "Strongly θ-b-continuous," Acta Math. Hunger.,110(4), pp.347-359, 2006.
22. S.Padmanaban, "On b- δ-open sets in topological spaces," Int Jr. of Mathematical Sciences & Applications,(3), pp.365-371, 2013.
23. J.Porter and J.Thomas, "On H-closed minimal Hausdorff spaces, "Trans.Amer.Math.Soc., 118, 159-170,1974.
24. U.Sengul, "on almost b-continuous functions, " Int. J. Contemp. Math. Sciences, 3(30), pp.1469-1480,2008.
25. M. Stone, "Applications of theory of Boolean rings to general topology,"Trans.Amer. Math. Soc.,(41),pp.375 – 381,1937.
26. N. V. Velicko, "H-closed topological spaces," Amer. Math. Soc. Transl., (78), pp.103 - 118, 1968.
27. I.Zorlutuna, "On b-closed spaces and θ-b-continuous functions, " The Arabian J. sci. eng., (34), pp. 205 – 216,2009.