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WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES

Year 2012, Volume: 41 Issue: 6, 785 - 793, 01.06.2012

Abstract

References

  • A¸cikg¨oz, A., Noiri, T. and Y¨uksel S¸. A decomposition of continuity in ideal topological spaces, Acta Math. Hungar. 105 (4), 285–289, 2004.
  • Chattopadhyay, K. C., Nj˚astad, K. C. and Thron W. J. Merotopic spaces and extensions of closure spaces, Can. J. Math. 35 (4), 613–629, 1983.
  • Chattopadhyay, K. C. and Thron, W. J. Extensions of closure spaces, Can. J. Math. 29 (6), –1286, 1977.
  • Choqet, G. Sur les notions de filter et grill, Comptes Rendus Acad. Sci. Paris 224, 171–173, Fomin, S. Extensions of topological spaces, Ann. of Math. 44, 471–480, 1943.
  • Hatir, E. and Jafari, S, On some new calsses of sets and a new decomposition of continuity via grills, J. Ads. Math. Studies. 3 (1), 33–40, 2010.
  • Jankovi´c, D. and Hamlet, T. R. New topologies from old via ideals, Amer. Math. Monthly , 295–310, 1990.
  • Kuratowski, K. Topology I (Academic Press, New York, 1966).
  • Levine, N. A decomposition of continuity in topological spaces, Amer Math. Monthly 68, –41, 1961.
  • Levine, N. Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly , 44–46, 1963.
  • Mashhour, A. S., Abd El-Monsef, M. E. and El-Deeb, S. N. On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47–53, 1982.
  • Renukadevi, V. Relation between ideals and grills, J. Adv. Res. Pure Math. 2 (4), 9–14, Rose, D. A. Weak continuity and almost continuity, Internat. J. Math. Math. Sci. 7, 311– , 1984.
  • Roy, B. and Mukherjee, M. N. On a typical topology induced by a grill, Soochow J. Math. (4), 771–786, 2007.
  • Thron, W. J. Proximity structure and grills, Math. Ann. 206, 35–62, 1973.
  • Vaidyanathaswamy, R. Set Topology (Chelsea Publishing Company, New York, 1960).

WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES

Year 2012, Volume: 41 Issue: 6, 785 - 793, 01.06.2012

Abstract

In this paper, we introduce and investigate the notion of a weakly Φcontinuous function in grill topological spaces and using this function we obtain a decomposition of continuity. Also, we investigate its relationship with other related functions.

References

  • A¸cikg¨oz, A., Noiri, T. and Y¨uksel S¸. A decomposition of continuity in ideal topological spaces, Acta Math. Hungar. 105 (4), 285–289, 2004.
  • Chattopadhyay, K. C., Nj˚astad, K. C. and Thron W. J. Merotopic spaces and extensions of closure spaces, Can. J. Math. 35 (4), 613–629, 1983.
  • Chattopadhyay, K. C. and Thron, W. J. Extensions of closure spaces, Can. J. Math. 29 (6), –1286, 1977.
  • Choqet, G. Sur les notions de filter et grill, Comptes Rendus Acad. Sci. Paris 224, 171–173, Fomin, S. Extensions of topological spaces, Ann. of Math. 44, 471–480, 1943.
  • Hatir, E. and Jafari, S, On some new calsses of sets and a new decomposition of continuity via grills, J. Ads. Math. Studies. 3 (1), 33–40, 2010.
  • Jankovi´c, D. and Hamlet, T. R. New topologies from old via ideals, Amer. Math. Monthly , 295–310, 1990.
  • Kuratowski, K. Topology I (Academic Press, New York, 1966).
  • Levine, N. A decomposition of continuity in topological spaces, Amer Math. Monthly 68, –41, 1961.
  • Levine, N. Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly , 44–46, 1963.
  • Mashhour, A. S., Abd El-Monsef, M. E. and El-Deeb, S. N. On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47–53, 1982.
  • Renukadevi, V. Relation between ideals and grills, J. Adv. Res. Pure Math. 2 (4), 9–14, Rose, D. A. Weak continuity and almost continuity, Internat. J. Math. Math. Sci. 7, 311– , 1984.
  • Roy, B. and Mukherjee, M. N. On a typical topology induced by a grill, Soochow J. Math. (4), 771–786, 2007.
  • Thron, W. J. Proximity structure and grills, Math. Ann. 206, 35–62, 1973.
  • Vaidyanathaswamy, R. Set Topology (Chelsea Publishing Company, New York, 1960).
There are 14 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Ahmad Al-omari This is me

Takashi Noiri This is me

Publication Date June 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 6

Cite

APA Al-omari, A., & Noiri, T. (2012). WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES. Hacettepe Journal of Mathematics and Statistics, 41(6), 785-793.
AMA Al-omari A, Noiri T. WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES. Hacettepe Journal of Mathematics and Statistics. June 2012;41(6):785-793.
Chicago Al-omari, Ahmad, and Takashi Noiri. “WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES”. Hacettepe Journal of Mathematics and Statistics 41, no. 6 (June 2012): 785-93.
EndNote Al-omari A, Noiri T (June 1, 2012) WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES. Hacettepe Journal of Mathematics and Statistics 41 6 785–793.
IEEE A. Al-omari and T. Noiri, “WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 6, pp. 785–793, 2012.
ISNAD Al-omari, Ahmad - Noiri, Takashi. “WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES”. Hacettepe Journal of Mathematics and Statistics 41/6 (June 2012), 785-793.
JAMA Al-omari A, Noiri T. WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES. Hacettepe Journal of Mathematics and Statistics. 2012;41:785–793.
MLA Al-omari, Ahmad and Takashi Noiri. “WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 6, 2012, pp. 785-93.
Vancouver Al-omari A, Noiri T. WEAKLY Φ-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES. Hacettepe Journal of Mathematics and Statistics. 2012;41(6):785-93.