ω-Topology and ⋆-Topology
Abstract
In this paper, we introduce some generalizations of !-open sets inideal topological spaces and investigate some properties of the sets. Moreover, we use them to obtain decompositions of continuity via idealization.
References
[1] M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, Beta-open sets and Beta-continuous mappings, Bull. Fac. Sci. Assuit Univ., 12(1)(1983), 77 - 90.
[2] A. Acikgoz, T. Noiri and S. Yuksel, On Alfa-I-continuous and Alfa-I-open functions, Acta Math.Hungar., 105(1-2)(2004), 27 - 37.
[3] A. Al-Omari and M. S. M. Noorani, Regular generalized !-closed sets, Intern. J. Math. Math. Sci., Volume 2007, Article ID 16292, 11 pages, doi: 10.1155/2007/16292.
[4] K. Al-Zoubi and B. Al-Nashef, The topology of !-open subsets, Al-Manareh, 2003, 9(2)(2003), 169 - 179.
[5] D. Andrijevic, On b-open sets, Mat. Vesnik, 1996, 48(1-2)(1996), 59 - 64.
[6] J. Dontchev, Idealization of Ganster Reilly Decomposition Theorems, arXiv:math/9901017 [math.GN]
[7] J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2(1996).
[8] E. Ekici and T. Noiri, ⋆-extremally disconnected ideal topological spaces, Acta Math. Hungar., 2009, 122(1-2)(2009), 81 - 90.
[9] A. C. Guler and G. Aslim, b-I-open sets and decomposition of continuity via idealization, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 22(2005), 27 - 32.
[10] E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar., 2002, 96(4)(2002), 341 - 349.
[11] E. Hatir, A. Keskin and T. Noiri, On a new decomposition of continuity via idealization, JP Jour. Geometry and Topology, 2003, 3(1)(2003), 53 - 64.
[12] H. Z. Hdeib, !-closed mappings, Revista Colomb. De Matem., 1982, 16(1-2)(1982), 65 - 78.
[13] H. Z. Hdeib, !-continuous functions, Dirasat, 1989, 16(2)(1989), 136 - 142.
[14] K. Kuratowski, Topology, Vol I. Academic Press (New York) 1966.
[15] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 1982, 53(1982), 47 - 53.
[16] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 1965, 15(1965), 961 - 970.
[17] T. Noiri, A. Al-Omari and M. S. M. Noorani, Weak forms of !-open sets and decompositions of continuity, Eur. J. Pure Appl. Math., 2(1)(2009), 73 - 84.
[18] R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., 20(1945), 51 - 61.
[19] R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, New York, 1946.
[20] S. Willard, General Topology, Addison-Wesley, Reading, Mass, USA, 1970.
[2] A. Acikgoz, T. Noiri and S. Yuksel, On Alfa-I-continuous and Alfa-I-open functions, Acta Math.Hungar., 105(1-2)(2004), 27 - 37.
[3] A. Al-Omari and M. S. M. Noorani, Regular generalized !-closed sets, Intern. J. Math. Math. Sci., Volume 2007, Article ID 16292, 11 pages, doi: 10.1155/2007/16292.
[4] K. Al-Zoubi and B. Al-Nashef, The topology of !-open subsets, Al-Manareh, 2003, 9(2)(2003), 169 - 179.
[5] D. Andrijevic, On b-open sets, Mat. Vesnik, 1996, 48(1-2)(1996), 59 - 64.
[6] J. Dontchev, Idealization of Ganster Reilly Decomposition Theorems, arXiv:math/9901017 [math.GN]
[7] J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2(1996).
[8] E. Ekici and T. Noiri, ⋆-extremally disconnected ideal topological spaces, Acta Math. Hungar., 2009, 122(1-2)(2009), 81 - 90.
[9] A. C. Guler and G. Aslim, b-I-open sets and decomposition of continuity via idealization, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 22(2005), 27 - 32.
[10] E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar., 2002, 96(4)(2002), 341 - 349.
[11] E. Hatir, A. Keskin and T. Noiri, On a new decomposition of continuity via idealization, JP Jour. Geometry and Topology, 2003, 3(1)(2003), 53 - 64.
[12] H. Z. Hdeib, !-closed mappings, Revista Colomb. De Matem., 1982, 16(1-2)(1982), 65 - 78.
[13] H. Z. Hdeib, !-continuous functions, Dirasat, 1989, 16(2)(1989), 136 - 142.
[14] K. Kuratowski, Topology, Vol I. Academic Press (New York) 1966.
[15] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 1982, 53(1982), 47 - 53.
[16] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 1965, 15(1965), 961 - 970.
[17] T. Noiri, A. Al-Omari and M. S. M. Noorani, Weak forms of !-open sets and decompositions of continuity, Eur. J. Pure Appl. Math., 2(1)(2009), 73 - 84.
[18] R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., 20(1945), 51 - 61.
[19] R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, New York, 1946.
[20] S. Willard, General Topology, Addison-Wesley, Reading, Mass, USA, 1970.
Downloads
Published
2017-01-01
Issue
Section
Чланци