Contra - Bc - Continuous Functions in Topological Spaces

Authors(3) :-Raja Mohammad Latif, Muhammad Rafiq Raja, Muhammad Razaq

In this paper by means of sets, we introduce and investigate certain ramifications of contra continuous and allied functions, namely,   almost  and almost  functions along with their several properties, characterizations and natural relationships. Further, we introduce new types of graphs, called and strongly graphs via sets. Several characterizations and properties of such notions are investigated.

Authors and Affiliations

Raja Mohammad Latif
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al-Khobar, Kingdom of Saudi Arabia
Muhammad Rafiq Raja
Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Pakistan
Muhammad Razaq
Department of Mathematics, Horizon Degree College and Commerce College, Bhaun Road, Chakwal, Pakistan

Almost, Contra – Bc – Continuous

  1. Raad Aziz Al-Abdulla and Ruaa Muslim Abed, On Bc – open sets, International Journal of Science and Research, Volume 3, Issue 10, (2014), 7 pages.
  2. Metin Akdag & Alkan Ozkan, Some Properties of Contra gb – continuous Functions, Journal of New Results in Science, 1 (2012) 40 – 49.
  3. D. Andrijevic, On b – open sets, Math. Vesnik, 48(1996), 59 – 64.
  4. G. Anitha and M. Mariasingam, Contra g ~ -WG Continuous Functions, International Journal of Computer Applications (0975 – 8887) Volume 49– No.11, (July 2012), 34 – 40.
  5. S. Balasubramanian, Almost contra vg-continuity, International Journal of Mathematical Engineering and Science, Volume 1 Issue 8 (August 2012), 51 – 65.
  6. M. Caldas and S. Jafari, Some properties of contra continuous functions, Mem. Fac. Sci. Kochi. Univ., Series A. Math., 22(2001), 19 – 28.
  7. J. Dontchev, Contra – continuous functions and strongly S – closed spaces, Internat. J. Math. Sci., 19(2) (1996), 303 – 310.
  8. J. Dontchev and T. Noiri, Contra-semi-continuous functions, Mathematica Pannonica, 10(2) (1999), 159-168.
  9. E. Ekici, Almost contra-precontinuous functions, Bull. Malaysian Math. Sci. Soc. , 27(1) (2004), pp. 53-65.
  10. E. Ekici and T. Noiri, Contra precontinuous functions, Bull. Cal. Math. Soc., 98(3) (2006), 275 – 284.
  11. E. Ekici, On contra -continuous functions, Chaos, Solitons and Fractals, 35(2008), 71 – 80.
  12. M. K. Gosh and C.K. Basu, Contra – e – Continuous functions, Gen. Math. Notes, Vol. 9, No.2, (2012), 1 – 18.
  13. Hariwan Z. Ibrahim, Bc-Open Sets in Topological Spaces, Advances in Pure Mathematics, Vol. 3, No. 1 (2013), 34 – 40.
  14. Hariwan Z. Ibrahim, Bc-Separation Axioms in Topological Spaces, Gen. Math. Notes, Vol. 17, No. 1 (2013), pp. 45 – 62.
  15. S. Jafari and T. Noiri, contra continuous functions between topological spaces, Iranian Int. J. Sci, 2(2001), 153 – 167.
  16.  S. Jafari and T. Noiri, On contra – precontinuous functions, Bull. Malaysian Math. Soc., 25(2002), 115 – 128.
  17. S. Jafari and T. Noiri, Contra – super – continuous functions, Annales Univ. Sci. Budapest 42(1999), 27 – 34.
  18. A.A. Nasef, Some properties of contra continuous functions, Chaos, Solitons and Fractals, 24(2005), 471 – 477.
  19. Govindappa Navalagi and S.M. Sjata, Some Contra – Continuous Functions via Pre – Open and Open Sets, International Journal of Mathematical Sciences & Applications, Vol. 2 Nr. 1 J. 2012, pp. 23 – 230.
  20. Neeran Tahir Al-Khafagy and Hanan Ali Hussein, bc – continuous function, Journal of Babylon University/Pure and Applied Sciences, Vol.21, No. 6, (2013), 1994 – 2000.
  21.  Mustafa H.J. and Muhammad S.K. and Al-Kafaji N.T. ,2010," αc-continuous function " ,Journal of kufa for Mathematics and Computer, Vol.1,No.1,April,pp.104 – 111.
  22. T. Noiri and V. Popa, Some properties of almost contra precontinuous functions, Bull. Malays. Math. Sci. Soc., 28 (2005), pp. 107-116.
  23.  A. Al-Omari and M.S. Md Noorani, Contra continuous and almost contra continuous, Internat. Jour. Math. Math. Sci., Article ID 40469, (2007) 13 pages.
  24.  A. Al – Omari and M.S. Md Noorani, Some properties of contra – b – continuous and almost contra – b – continuous functions, European Jour. Pure. Appl. Math., 2(2) (2009), 213 – 220.
  25.  Murad ¨Ozkoc and G¨ulhan Asl?m, On weakly – e – continuous functions, Hacettepe Journal of Mathematics and Statistics, Volume 40 (6) (2011), 781 – 791.
  26. N. Rajesh. On total Continuity, Strong Continuity and contra Continuity, Soochow Journal of Mathematics,2007, 33.4:679-690.
  27. S. Sekar and R. Brindha, Almost Contra Pre – Generlized b – Continuous Functions in Topological Spaces, Malaya Journal of Matematik , 5(2) (2017) 194 – 201.
  28.  R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169 – 185.
  29. Appachi Vadivel, Radhakrishnan Ramesh and Duraisamy Sivakumar, Contra continuous and almost contra continuous functions, Sahand Communications in Mathematical Analysis, Vol. 8, No. 1 (2017), 55 – 71.
  30. M.K.R.S.Veerakumar, Contra – Pre – Semi – Continuity. B.M.M.S.S., (2005 ) 28 (1):67 – 71.
  31.  Stephen Willard, General Topology, Addison Wesley, 1970.

Publication Details

Published in : Volume 4 | Issue 9 | July-August 2018
Date of Publication : 2018-06-30
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 18-29
Manuscript Number : IJSRST1848246
Publisher : Technoscience Academy

Print ISSN : 2395-6011, Online ISSN : 2395-602X

Cite This Article :

Raja Mohammad Latif, Muhammad Rafiq Raja, Muhammad Razaq, " Contra - Bc - Continuous Functions in Topological Spaces ", International Journal of Scientific Research in Science and Technology(IJSRST), Print ISSN : 2395-6011, Online ISSN : 2395-602X, Volume 4, Issue 9, pp.18-29, July-August-2018.
Journal URL : https://ijsrst.com/IJSRST1848246
Citation Detection and Elimination     |      | |
  • T. Noiri and V. Popa, Some properties of almost contra precontinuous functions, Bull. Malays. Math. Sci. Soc., 28 (2005), pp. 107-116.
  •  A. Al-Omari and M.S. Md Noorani, Contra continuous and almost contra continuous, Internat. Jour. Math. Math. Sci., Article ID 40469, (2007) 13 pages.
  •  A. Al – Omari and M.S. Md Noorani, Some properties of contra – b – continuous and almost contra – b – continuous functions, European Jour. Pure. Appl. Math., 2(2) (2009), 213 – 220.
  •  Murad ¨Ozkoc and G¨ulhan Asl?m, On weakly – e – continuous functions, Hacettepe Journal of Mathematics and Statistics, Volume 40 (6) (2011), 781 – 791.
  • N. Rajesh. On total Continuity, Strong Continuity and contra Continuity, Soochow Journal of Mathematics,2007, 33.4:679-690.
  • S. Sekar and R. Brindha, Almost Contra Pre – Generlized b – Continuous Functions in Topological Spaces, Malaya Journal of Matematik , 5(2) (2017) 194 – 201.
  •  R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169 – 185.
  • Appachi Vadivel, Radhakrishnan Ramesh and Duraisamy Sivakumar, Contra continuous and almost contra continuous functions, Sahand Communications in Mathematical Analysis, Vol. 8, No. 1 (2017), 55 – 71.
  • M.K.R.S.Veerakumar, Contra – Pre – Semi – Continuity. B.M.M.S.S., (2005 ) 28 (1):67 – 71.
  •  Stephen Willard, General Topology, Addison Wesley, 1970.
  • " target="_blank"> BibTeX
    |
  • T. Noiri and V. Popa, Some properties of almost contra precontinuous functions, Bull. Malays. Math. Sci. Soc., 28 (2005), pp. 107-116.
  •  A. Al-Omari and M.S. Md Noorani, Contra continuous and almost contra continuous, Internat. Jour. Math. Math. Sci., Article ID 40469, (2007) 13 pages.
  •  A. Al – Omari and M.S. Md Noorani, Some properties of contra – b – continuous and almost contra – b – continuous functions, European Jour. Pure. Appl. Math., 2(2) (2009), 213 – 220.
  •  Murad ¨Ozkoc and G¨ulhan Asl?m, On weakly – e – continuous functions, Hacettepe Journal of Mathematics and Statistics, Volume 40 (6) (2011), 781 – 791.
  • N. Rajesh. On total Continuity, Strong Continuity and contra Continuity, Soochow Journal of Mathematics,2007, 33.4:679-690.
  • S. Sekar and R. Brindha, Almost Contra Pre – Generlized b – Continuous Functions in Topological Spaces, Malaya Journal of Matematik , 5(2) (2017) 194 – 201.
  •  R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169 – 185.
  • Appachi Vadivel, Radhakrishnan Ramesh and Duraisamy Sivakumar, Contra continuous and almost contra continuous functions, Sahand Communications in Mathematical Analysis, Vol. 8, No. 1 (2017), 55 – 71.
  • M.K.R.S.Veerakumar, Contra – Pre – Semi – Continuity. B.M.M.S.S., (2005 ) 28 (1):67 – 71.
  •  Stephen Willard, General Topology, Addison Wesley, 1970.
  • " target="_blank">RIS
    |
  • T. Noiri and V. Popa, Some properties of almost contra precontinuous functions, Bull. Malays. Math. Sci. Soc., 28 (2005), pp. 107-116.
  •  A. Al-Omari and M.S. Md Noorani, Contra continuous and almost contra continuous, Internat. Jour. Math. Math. Sci., Article ID 40469, (2007) 13 pages.
  •  A. Al – Omari and M.S. Md Noorani, Some properties of contra – b – continuous and almost contra – b – continuous functions, European Jour. Pure. Appl. Math., 2(2) (2009), 213 – 220.
  •  Murad ¨Ozkoc and G¨ulhan Asl?m, On weakly – e – continuous functions, Hacettepe Journal of Mathematics and Statistics, Volume 40 (6) (2011), 781 – 791.
  • N. Rajesh. On total Continuity, Strong Continuity and contra Continuity, Soochow Journal of Mathematics,2007, 33.4:679-690.
  • S. Sekar and R. Brindha, Almost Contra Pre – Generlized b – Continuous Functions in Topological Spaces, Malaya Journal of Matematik , 5(2) (2017) 194 – 201.
  •  R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169 – 185.
  • Appachi Vadivel, Radhakrishnan Ramesh and Duraisamy Sivakumar, Contra continuous and almost contra continuous functions, Sahand Communications in Mathematical Analysis, Vol. 8, No. 1 (2017), 55 – 71.
  • M.K.R.S.Veerakumar, Contra – Pre – Semi – Continuity. B.M.M.S.S., (2005 ) 28 (1):67 – 71.
  •  Stephen Willard, General Topology, Addison Wesley, 1970.
  • " target="_blank">CSV

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