Pre-regular \(sp\)-open sets in topological spaces
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P. Jeyanthi
jeyajeyanthi@rediffmail.com
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P. Nalayini
nalayini4@gmail.com
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T. Noiri
t.noiri@nifty.com
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DOI:
https://doi.org/10.4067/S0719-06462018000100031Abstract
In this paper, a new class of generalized open sets in a topological space, called pre- regular sp-open sets, is introduced and studied. This class is contained in the class of semi-preclopen sets and cotains all pre-clopen sets. We obtain decompositions of regular open sets by using pre-regular sp-open sets.
Keywords
[1] M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77-90.
[2] D. Andrijevic, Semi-preopen sets, Mat. Vesnik., 38 (1986), 24-32.
[3] D. Andrijevic, On b-open sets, Mat. Vesnik., 48 (1996), 59-64.
[4] S. P. Arya and R. Gupta, On strongly continuous mappings, Kyungpook Math. J., 14 (1947),131-143.
[5] C. Chattopadhyay and C. Bandyopadhyay, On structure of δ-sets, Bull. Calcutta Math. Soc., 83 (2011), 281-290.
[6] J. Dugundji, Topology, Allyn and Bacon, Boston (1966).
[7] M. Ganster and D. Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math.Comp. Sci. (Math. Ser.) 1 (2) (1988), 65-75.
[8] I. A. Hasanein, M. E. Abd El-Monsef and S. N. El-Deep, α-continuity andα-open mappings, Acta. Math. Hungar., 41 (1983), 213-218.
[9] S. Jafari, On certain types of notions via preopen sets, Tamkang J. Math., 37 (4) (2006),391-398.
[10] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly,70 (1963), 36-41.
[11] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deep, On precontinuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt., 53 (1982), 47-53.
[12] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.
[13] M. Stone, Applications of the theory of boolean ring to general topology, Trans. Amer. Math.Soc., 41 (1937), 374.
[14] P. Thangavelu and K. C. Rao, q-sets in topological spaces, Prog of Maths., 36 (1-2) (2002),159-165.
[2] D. Andrijevic, Semi-preopen sets, Mat. Vesnik., 38 (1986), 24-32.
[3] D. Andrijevic, On b-open sets, Mat. Vesnik., 48 (1996), 59-64.
[4] S. P. Arya and R. Gupta, On strongly continuous mappings, Kyungpook Math. J., 14 (1947),131-143.
[5] C. Chattopadhyay and C. Bandyopadhyay, On structure of δ-sets, Bull. Calcutta Math. Soc., 83 (2011), 281-290.
[6] J. Dugundji, Topology, Allyn and Bacon, Boston (1966).
[7] M. Ganster and D. Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math.Comp. Sci. (Math. Ser.) 1 (2) (1988), 65-75.
[8] I. A. Hasanein, M. E. Abd El-Monsef and S. N. El-Deep, α-continuity andα-open mappings, Acta. Math. Hungar., 41 (1983), 213-218.
[9] S. Jafari, On certain types of notions via preopen sets, Tamkang J. Math., 37 (4) (2006),391-398.
[10] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly,70 (1963), 36-41.
[11] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deep, On precontinuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt., 53 (1982), 47-53.
[12] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.
[13] M. Stone, Applications of the theory of boolean ring to general topology, Trans. Amer. Math.Soc., 41 (1937), 374.
[14] P. Thangavelu and K. C. Rao, q-sets in topological spaces, Prog of Maths., 36 (1-2) (2002),159-165.
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Published
2018-10-19
How to Cite
[1]
P. Jeyanthi, P. Nalayini, and T. Noiri, “Pre-regular \(sp\)-open sets in topological spaces”, CUBO, vol. 20, no. 1, pp. 31–39, Oct. 2018.
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