The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

P-I-OPEN MAPPINGS, P-I-CONTINUOUS MAPPINGS AND P-I-IRRESOLUTE MAPPINGS

  • Kim, Ji-Yoon (DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY) ;
  • Kim, Chang-Su (DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY)
  • Published : 2009.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

The notions of P-I-open (closed) mappings, P-I-continuous mappings, P-I-neighborhoods, P-I-irresolute mappings and I-irresolute mappings are introduced. Relations between P-I-open (closed) mappings and I-open (closed) mappings are given. Characterizations of P-I-open (closed) mappings are provided. Relations between a P-I-continuous mapping and an I-continuous mapping are discussed, and characterizations of a P-I-continuous mapping are considered. Conditions for a mapping to be an I-irresolute mapping (resp. P-I-irresolute mapping) are provided.

Keywords

References

  1. M.E. Abd El-Monsef, E.F. Lashien & A.A. Nasef: On I-open sets and I-continious funtions. Kyungpook. Math. J. 32 (1992), 21-30.
  2. A. Acikgoz, T. Noiri & S. Yuksel: On ${\delta}-I-open$ sets and decomposition of ${\alpha}-I-continuity$. Acta Math. Hungar. 102 (2004), no. 4, 349-357. https://doi.org/10.1023/B:AMHU.0000024685.84429.e9
  3. A. Acikgoz, T. Noiri & S. Yuksel: On ${\alpha}-I-continuous$and ${\alpha}-I-open$ functions. Acta Math. Hungar. 105 (2004), no. 1-2, 27-37. https://doi.org/10.1023/B:AMHU.0000045530.79591.d5
  4. D. Andrijevic: On b-open sets. Mat. Vesnik 48, (1996), 59-64.
  5. D. Andrijevic: Some properties of the topology of ${\alpha}-sets$. Mat. Vesnik 36 (1984), 1-10.
  6. M. Akdag: On b-I-open sets and b-I -continuous functions. Internat. J. Math. Math. Sci. 2007 Article ID 75721, 13 pages.
  7. M. Caldas: A note on some applications of ${\alpha}-sets$. Int. J. Math. Math. Sci. 2003 (2003), no. 2, 125-130. https://doi.org/10.1155/S0161171203203161
  8. M. Caldas & J. Dontchev: On spaces with hereditarily compact ${\alpha}-topologies$. Acta Math. Hung. 82 (1999), 121-129. https://doi.org/10.1023/A:1026450024704
  9. E. Hatir, A. Keskin & T. Noiri: A note on strong ${\beta}-I-open$ sets and strongly ${\beta}-I-continuous$ functions Acta Math. Hungar. 108 (2005), no. 1-2, 87-94. https://doi.org/10.1007/s10474-005-0210-2
  10. E. Hatir & T. Noiri: On decompositions of continuity via idealization. Acta Math. Hungar. 96 (2002), no. 4, 341-349. https://doi.org/10.1023/A:1019760901169
  11. E. Hatir & T. Noiri: Weakly pre-I-open sets and decomposition of continuity. Acta Math. Hungar. 106 (2005) , no. 3, 227-238. https://doi.org/10.1007/s10474-005-0015-3
  12. E. Hatir & T. Noiri: On semi-I-open sets and semi-I-continuous functions. Acta Math. Hungar. 107 (2005), no. 4, 345-353. https://doi.org/10.1007/s10474-005-0202-2
  13. E. Hatir & T. Noiri: On ${\beta}-I-open$ sets and a decomposition of almost-I-continuity. Bull. Malay. Math. Sci. Soc. 29 (2006), no. 2, 119-124.
  14. S. Jafari & T. Noiri: $Contra-{\alpha}-continuous$ functions between topological spaces. Iranian Int. J. Sci. 2 (2001), no. 2, 153-167.
  15. S. Jafari & T. Noiri: Some remarks on weak ${\alpha}-continuity$. Far East J. Math. Sci. 6 (1998), no. 4, 619-625.
  16. D. Jankovic & T. R. Hamlett: New topologies from old via ideals. Amer. Math. Monthly 97(4) (1990), 295-310. https://doi.org/10.2307/2324512
  17. Y.B. Jun, S.W. Jeong, H.J. Lee & J.W. Lee: Application of pre-open sets. Appl. General Top. 9 (2008), no. 2, 213-228. https://doi.org/10.4995/agt.2008.1802
  18. J.G. Kang & C.S. Kim: On P-I-open sets. Honam Math. J. (to appear).
  19. N. Levine: Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.2307/2312781
  20. S.N. Maheshwari & S.S. Thakur: On ${\alpha}-irresolute$ mappings. Tamkang J. Math. 11 (1980), 209-214.
  21. S.N. Maheshwari & S.S. Thakur: On ${\alpha}-compact$ spaces. Bull. Inst. Math. Acad. Sinica 13 (1985), 341-347.
  22. H. Maki, R. Devi & K. Balachandran: Generalized ${\alpha}-closed$ sets in topology. Bull. Fukuoka Univ. Ed. Part III 42 (1993), 13-21.
  23. H. Maki & T. Noiri: The pasting lemma for ${\alpha}-continuous$ maps. Glas. Mat. 23 (1988), no. 43, 357-363.
  24. A.S. Mashhour, I.A. Hasanein & S.N. El-Deeb: A note on semi-continuity and precontinuity. Indian J. Pure Appl. Math. 13 (1982), no. 10, 1119-1123.
  25. A.S. Mashhour, I.A. Hasanein & S.N. El-Deeb: ${\alpha}-continuous$ and ${\alpha}-open$ mappings. Acta Math. Hungar. 41 (1983), no. 3-4, 213-218. https://doi.org/10.1007/BF01961309
  26. O. Njastad: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
  27. I.L. Reilly & M.K. Vamanamurthy: On ${\alpha}-sets$ in topological spaces. Tamkang J. Math. 16 (1985), 7-11.
  28. J. Tong: On decomposition of continuity in topological spaces. Acta Math. Hungar. 54 (1989), no. 1-2, 51-55. https://doi.org/10.1007/BF01950708