Remarks on δ-semi-open sets and δ-preopen sets

Demonstratio Mathematica

Volumn 36, Issue 4, 2003, Pages 1007-1020

  Noiri, Takashi ^a  

^a KUMAMOTO NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

Author keywords

Preopen; S closed; Semi open; Semi regularization; Semiconnected; preopen; semi open

Indexed keywords

EID: 33751169326     PISSN: 04201213     EISSN: 23914661     Source Type: Journal    
DOI: 10.1515/dema-2003-0424     Document Type: Article

References (43)

1. M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12(1983), 77-90.
2. M. E. Abd El-Monsef, R. A. Mahmoud and E. R. Lashin, β-closure and β-interior, J. Fac. Ed. Ain Shams Univ. 10(1986), 235-245.
3. D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38(1986), 24-32.
4. S. P. Arya, M. P. Bhamini, Some generalizations of pairwise Urysohn spaces, Indian J. Pure Appl. Math. 18(1987), 1088-1093.
5. N. Biswas, On characterizations of semi-continuous functions, Atti Accad. Naz. Lincei Rend. Cl. Sei. Fis. Mat. Natur. (8) 48(1970), 399-402.
6. D. E. Cameron, Properties of S-closed spaces, Proc. Amer. Math. Soc. 72(1978), 581-586.
7. S. G. Crossley, S. K. Hildebrand, Semi-closure, Texas J. Sei. 22(1971), 99-112.
8. S. G. Crossley, S. K. Hildebrand, Semi-topological properties, Fund. Math. 74(1972), 233-254.
9. A. Debray, Investigations of Some Problems of Topology and Certain Allied Structures, Ph. D. Thesis, Univ. of Calcutta, 1999.
10. G. Di Maio, T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math. 18(1987), 226-233.
11. G. Di Maio, T. Noiri, Weak and strong forms of irresolute functions, Suppl. Rend. Circ. Mat. Palermo (2) 18(1988), 255-273.
12. J. Dontchev, M. Ganster, T. Noiri, On p-closed spaces, Internat. J. Math. Math. Sci. 24(2000), 203-212.
13. C. Dorsett, Semi-regular spaces, Soochow J. Math. 8(1982), 45-53.
14. C. Dorsett, Semi-normal spaces, Kyungpook Math. J. 25(1985), 173-180.
15. S. N. El-Deeb, I. A. Hasanein, A. S. Mashhour and T. Noiri, On p-regular spaces, Bull. Math. Soc. Sei. Math. R. S. Roumanie 27(75) (1983), 311-315.
16. T. Husain, Almost continuous mappings, Prace Mat. 10(1966), 1-7.
17. B. Y. Lee, M. J. Son and J. H. Park, 5-semi-open sets and its applications, Far East J. Math. Sci. 3(5) (2001), 745-759.
18. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70(1963), 36-41.
19. N. Levine, Dense topologies, Amer. Math. Monthly 75(1968), 847-852.
20. S. Marcus, Sur les fonctions quasicontinues au sens de S. Kempisty, Colloq. Math. 8(1961), 47-53.
21. S. Maheshwari, R. Prasad, On s-regular spaces, Glasnik Mat. 10(30) (1970), 347-350.
22. S. Maheshwari, R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelles 89(1975), 395-402.
23. S. Maheshwari, R. Prasad, On s-normal spaces, Bull. Math. Soc. Sei. Math. R. S. Roumanie (N. S.) 22(68) (1978), 27-29.
24. A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deep, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53(1982), 47-53.
25. A. S. Mashhour, M. E. Abd El-Monsef, I. A. Hasanein and T. Noiri, Strongly compact spaces, Delta J. Sci. 8(1984), 30-46.
26. A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semi-continuity and precontinuity, Indian J. Pure Appl. Math. 13(1982), 1119-1123.
27. A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, α-continuous and a-open mappings, Acta Math. Hungar. 41(1983), 213-218.
28. M. Mrševic, I. L. Reilly and M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc., Ser. A, 38(1985), 40-54.
29. B. M. Munshi, D. S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13(1982), 229-236.
30. A. Neubrunnová, On certain generalizations of the notion of continuity, Mat. Časopis 23(1973), 374-380.
31. O. Njâstad, On some classes of nearly open sets, Pacific J. Math. 15(1965), 961-970.
32. T. Noiri, On semi-continuous mappings, Atti Accad. Naz. Lincei Rend. Cl. Sei. Fis. Mat. Natur. (8) 54(1973), 210-214.
33. T. Noiri, A note on hyperconnected sets, Mat. Vesnik 3(16) (31) (1979), 53-60.
34. J. H. Park, B. Y. Lee and M. J. Son, On δ-semiopen sets in topological spaces, J. Indian Acad. Math. 19(1997), 59-67.
35. V. Pipitone, G. Russo, Spazi semiconnessi e spazi semiaperti, Rend. Circ. Mat. Palermo (2) 24(1975), 273-285.
36. V. Popa, Properties of H-almost continuous functions, Bull. Math. Soc. Sei. Math. R. S. Roumanie (N. S.) 31(79) (1987), 163-168.
37. ∗-almost continuity and S-preregularity, Bull. Calcutta Math. Soc. 85(1993), 385-392.
38. S. Raychaudhuri, M. N. Mukherjee, On δ-almost continuity and S-preopen sets, Bull. Inst. Math. Acad. Sinica 21(1993), 357-366.
39. S. Raychaudhuri, M. N. Mukherjee, Further characterizations of Sp-closed spaces, J. Pure Math. 12(1995), 27-35.
40. p-closedness for topological spaces, J. Indian Acad. Math. 18(1996), 89-99.
41. I. L. Reilly, M. K. Vamanamurthy, On a-continuity in topological spaces, Acta Math. Hungar. 45(1985), 27-32.
42. L. A. Steen, J. A. Seebach, Counterexamples in Topology, Holt, Reinhart and Winstan, Inc., New York, 1970.
43. N. V. Velièko, H-closed topological spaces, Amer. Math. Soc. Transl. (2) 78(1968), 103-118.