(i,j) - Sc - Continuous and (i,j) - θSc - continuous Functions
Keywords:
(i,j) - Sc - continuous, (i,j) - θSc - continuous, Semi – continuousAbstract
In this paper, we introduce new types of continuity in bitopological spaces called (i,j) - Sc - continuous and (i,j) - θSc - continuous. We discuss the relationship between these types of continuity and other known types of continuous functions.
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References
- Arya S. P. and Bhamini M. P., (1982), A note on Semi – US spaces, Ranchi Univ. Maths.
J., 13 60 – 69.
- Carnahan D. A. (1973), Some Properties Related to Compactness in Topological Spaces, Ph. D.
Thesis, Univ. of Arkansas,.
- Crossely S. G. and Hildebrand S. K., (1971), Semi – closure, Texas J. Sci., 22, 99 –112.
- Di Maio G. and Noiri T., (1987), On s – closed spaces, Indian J. pure Appl. Math.,
18(3), 226 – 233.
- Dontchev J., (1998), Survy on preopen sets, The proceedings of the Yatsushiro Topological
Conference , 1 – 18.
- Dontchev J. and Noiri T., (1999), Contra semi – continuous functions, Math. Pannon, 10(2), 159 – 168.
- Dontchev J., Ganster M. and Noiri T., (2000), On p – closed spaces, Internat J. Math. Math.
Sci., 2(3), 203 – 212.
- El – Deeb S. N., Hasanein I. A., Mashhour A. S. and Noiri T., (1983), On p – regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roum., 27(4) 311 – 315.
- Ganster M., Noiri T. and Reilly I. L., (1988), Weak and strong forms of θ- irresolute functions, J. Inst. Math. Comput. Sci., 1(1) 19 – 29.
- Ganster M., (1990), On stongly s – regular spaces, Glasnik Mat., 25(45) 195 – 201.
- Hardi N. A., (2012), (i,j)-S_c- open set in bitopological spaces, Int. J. of Scientific and
Engineering research, 3(10).
- Jankovic D. S., (1985), A note on mappings of extermally disconnected spaces, Acta Math.
Hungar., 46(1 – 2) 83 – 92.
- Joseph J. E. and Kwack M. H., (1980), On S – closed spaces, Proc. Amer. Math. Soc.,
80(2) 341 – 348.
- Kelley J. C., (1963), Bitopological spaces, Proc. London Math. Soc., 13(3) 71-89.
- Khalaf A. B. and Easif F. H., (1999), θs-continuous functions, J. Dohuk Univ. (Special issue) 2(1) 1 – 7.
- Kheder F. H. and Noiri T., (1986), On θ- irresolute functions, Indian J. Math., 28(3) 211 – 217.
- Levine N., (1963), Semi–open sets and semi – continuity in topological spaces, Amer. Math. Monthly, 70(1) 36 – 41.
- Mashhour A. S., Abd El – Monsef M. E. and El –Deeb S. N., (1982), On precontinuous and weak precontinuous mappings, Proc. Math. phys. Soc. Egypt, 53 47 – 53.
- Park J. H. and Park Y. B., (1995), Weaker forms of irresolute functions, Indian J. pure Appl. Math., 26(7) 691 – 696.
- Stone M. H., (1937), Algebraic Characterizations of special Boolean rings, fund. Math., (29), 223 – 302.
- Stone M. H., (1937), Applications of the theory of Boolean rings to topology, Trans. Amer.
Math. Soc., (41), 375 – 481.
- Velicko N. V., (1968), H – closed topological spaces, Amer. Math. Soc. Transl., 78(2), 103 – 118.
- Arya S. P. and Bhamini M. P., (1982), A note on Semi – US spaces, Ranchi Univ. Maths.
J., 13 60 – 69.
- Carnahan D. A. (1973), Some Properties Related to Compactness in Topological Spaces, Ph. D.
Thesis, Univ. of Arkansas,.
- Crossely S. G. and Hildebrand S. K., (1971), Semi – closure, Texas J. Sci., 22, 99 –112.
- Di Maio G. and Noiri T., (1987), On s – closed spaces, Indian J. pure Appl. Math.,
18(3), 226 – 233.
- Dontchev J., (1998), Survy on preopen sets, The proceedings of the Yatsushiro Topological
Conference , 1 – 18.
- Dontchev J. and Noiri T., (1999), Contra semi – continuous functions, Math. Pannon, 10(2), 159 – 168.
- Dontchev J., Ganster M. and Noiri T., (2000), On p – closed spaces, Internat J. Math. Math.
Sci., 2(3), 203 – 212.
- El – Deeb S. N., Hasanein I. A., Mashhour A. S. and Noiri T., (1983), On p – regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roum., 27(4) 311 – 315.
- Ganster M., Noiri T. and Reilly I. L., (1988), Weak and strong forms of θ- irresolute functions, J. Inst. Math. Comput. Sci., 1(1) 19 – 29.
- Ganster M., (1990), On stongly s – regular spaces, Glasnik Mat., 25(45) 195 – 201.
- Hardi N. A., (2012), (i,j)-S_c- open set in bitopological spaces, Int. J. of Scientific and
Engineering research, 3(10).
- Jankovic D. S., (1985), A note on mappings of extermally disconnected spaces, Acta Math.
Hungar., 46(1 – 2) 83 – 92.
- Joseph J. E. and Kwack M. H., (1980), On S – closed spaces, Proc. Amer. Math. Soc.,
80(2) 341 – 348.
- Kelley J. C., (1963), Bitopological spaces, Proc. London Math. Soc., 13(3) 71-89.
- Khalaf A. B. and Easif F. H., (1999), θs-continuous functions, J. Dohuk Univ. (Special issue) 2(1) 1 – 7.
- Kheder F. H. and Noiri T., (1986), On θ- irresolute functions, Indian J. Math., 28(3) 211 – 217.
- Levine N., (1963), Semi–open sets and semi – continuity in topological spaces, Amer. Math. Monthly, 70(1) 36 – 41.
- Mashhour A. S., Abd El – Monsef M. E. and El –Deeb S. N., (1982), On precontinuous and weak precontinuous mappings, Proc. Math. phys. Soc. Egypt, 53 47 – 53.
- Park J. H. and Park Y. B., (1995), Weaker forms of irresolute functions, Indian J. pure Appl. Math., 26(7) 691 – 696.
- Stone M. H., (1937), Algebraic Characterizations of special Boolean rings, fund. Math., (29), 223 – 302.
- Stone M. H., (1937), Applications of the theory of Boolean rings to topology, Trans. Amer.
Math. Soc., (41), 375 – 481.
- Velicko N. V., (1968), H – closed topological spaces, Amer. Math. Soc. Transl., 78(2), 103 – 118.
J., 13 60 – 69.
- Carnahan D. A. (1973), Some Properties Related to Compactness in Topological Spaces, Ph. D.
Thesis, Univ. of Arkansas,.
- Crossely S. G. and Hildebrand S. K., (1971), Semi – closure, Texas J. Sci., 22, 99 –112.
- Di Maio G. and Noiri T., (1987), On s – closed spaces, Indian J. pure Appl. Math.,
18(3), 226 – 233.
- Dontchev J., (1998), Survy on preopen sets, The proceedings of the Yatsushiro Topological
Conference , 1 – 18.
- Dontchev J. and Noiri T., (1999), Contra semi – continuous functions, Math. Pannon, 10(2), 159 – 168.
- Dontchev J., Ganster M. and Noiri T., (2000), On p – closed spaces, Internat J. Math. Math.
Sci., 2(3), 203 – 212.
- El – Deeb S. N., Hasanein I. A., Mashhour A. S. and Noiri T., (1983), On p – regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roum., 27(4) 311 – 315.
- Ganster M., Noiri T. and Reilly I. L., (1988), Weak and strong forms of θ- irresolute functions, J. Inst. Math. Comput. Sci., 1(1) 19 – 29.
- Ganster M., (1990), On stongly s – regular spaces, Glasnik Mat., 25(45) 195 – 201.
- Hardi N. A., (2012), (i,j)-S_c- open set in bitopological spaces, Int. J. of Scientific and
Engineering research, 3(10).
- Jankovic D. S., (1985), A note on mappings of extermally disconnected spaces, Acta Math.
Hungar., 46(1 – 2) 83 – 92.
- Joseph J. E. and Kwack M. H., (1980), On S – closed spaces, Proc. Amer. Math. Soc.,
80(2) 341 – 348.
- Kelley J. C., (1963), Bitopological spaces, Proc. London Math. Soc., 13(3) 71-89.
- Khalaf A. B. and Easif F. H., (1999), θs-continuous functions, J. Dohuk Univ. (Special issue) 2(1) 1 – 7.
- Kheder F. H. and Noiri T., (1986), On θ- irresolute functions, Indian J. Math., 28(3) 211 – 217.
- Levine N., (1963), Semi–open sets and semi – continuity in topological spaces, Amer. Math. Monthly, 70(1) 36 – 41.
- Mashhour A. S., Abd El – Monsef M. E. and El –Deeb S. N., (1982), On precontinuous and weak precontinuous mappings, Proc. Math. phys. Soc. Egypt, 53 47 – 53.
- Park J. H. and Park Y. B., (1995), Weaker forms of irresolute functions, Indian J. pure Appl. Math., 26(7) 691 – 696.
- Stone M. H., (1937), Algebraic Characterizations of special Boolean rings, fund. Math., (29), 223 – 302.
- Stone M. H., (1937), Applications of the theory of Boolean rings to topology, Trans. Amer.
Math. Soc., (41), 375 – 481.
- Velicko N. V., (1968), H – closed topological spaces, Amer. Math. Soc. Transl., 78(2), 103 – 118.
- Arya S. P. and Bhamini M. P., (1982), A note on Semi – US spaces, Ranchi Univ. Maths.
J., 13 60 – 69.
- Carnahan D. A. (1973), Some Properties Related to Compactness in Topological Spaces, Ph. D.
Thesis, Univ. of Arkansas,.
- Crossely S. G. and Hildebrand S. K., (1971), Semi – closure, Texas J. Sci., 22, 99 –112.
- Di Maio G. and Noiri T., (1987), On s – closed spaces, Indian J. pure Appl. Math.,
18(3), 226 – 233.
- Dontchev J., (1998), Survy on preopen sets, The proceedings of the Yatsushiro Topological
Conference , 1 – 18.
- Dontchev J. and Noiri T., (1999), Contra semi – continuous functions, Math. Pannon, 10(2), 159 – 168.
- Dontchev J., Ganster M. and Noiri T., (2000), On p – closed spaces, Internat J. Math. Math.
Sci., 2(3), 203 – 212.
- El – Deeb S. N., Hasanein I. A., Mashhour A. S. and Noiri T., (1983), On p – regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roum., 27(4) 311 – 315.
- Ganster M., Noiri T. and Reilly I. L., (1988), Weak and strong forms of θ- irresolute functions, J. Inst. Math. Comput. Sci., 1(1) 19 – 29.
- Ganster M., (1990), On stongly s – regular spaces, Glasnik Mat., 25(45) 195 – 201.
- Hardi N. A., (2012), (i,j)-S_c- open set in bitopological spaces, Int. J. of Scientific and
Engineering research, 3(10).
- Jankovic D. S., (1985), A note on mappings of extermally disconnected spaces, Acta Math.
Hungar., 46(1 – 2) 83 – 92.
- Joseph J. E. and Kwack M. H., (1980), On S – closed spaces, Proc. Amer. Math. Soc.,
80(2) 341 – 348.
- Kelley J. C., (1963), Bitopological spaces, Proc. London Math. Soc., 13(3) 71-89.
- Khalaf A. B. and Easif F. H., (1999), θs-continuous functions, J. Dohuk Univ. (Special issue) 2(1) 1 – 7.
- Kheder F. H. and Noiri T., (1986), On θ- irresolute functions, Indian J. Math., 28(3) 211 – 217.
- Levine N., (1963), Semi–open sets and semi – continuity in topological spaces, Amer. Math. Monthly, 70(1) 36 – 41.
- Mashhour A. S., Abd El – Monsef M. E. and El –Deeb S. N., (1982), On precontinuous and weak precontinuous mappings, Proc. Math. phys. Soc. Egypt, 53 47 – 53.
- Park J. H. and Park Y. B., (1995), Weaker forms of irresolute functions, Indian J. pure Appl. Math., 26(7) 691 – 696.
- Stone M. H., (1937), Algebraic Characterizations of special Boolean rings, fund. Math., (29), 223 – 302.
- Stone M. H., (1937), Applications of the theory of Boolean rings to topology, Trans. Amer.
Math. Soc., (41), 375 – 481.
- Velicko N. V., (1968), H – closed topological spaces, Amer. Math. Soc. Transl., 78(2), 103 – 118.
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Published
2013-06-30
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Science Journal of University of Zakho
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Copyright (c) 2013 ALIAS B. KHALAF, Hardi N. Aziz, Hardi A. Sharef
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How to Cite
KHALAF, A. B., Aziz, H. N., & Sharef, H. A. (2013). (i,j) - Sc - Continuous and (i,j) - θSc - continuous Functions. Science Journal of University of Zakho, 1(1), 338-348. https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/114
