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More on α-topological spaces

Year 2017, Volume: 66 Issue: 2, 323 - 331, 01.08.2017
https://doi.org/10.1501/Commua1_0000000822

Abstract

The aim of this paper is to introduce a new topology with the help of a-open sets. For this job, we shall define two new types of set and discuss its properties in detail and characterize Njastad’ssemi-open sets through these new types of set.-open sets and Levine’s

References

  • Al-Omari, W., Noorani, M., Noiri, T. and Al-Omari, A.: The
  • Al-Omari, W., Noorani, M. and Al-Omari, A.: a-local function and its properties in ideal topological spaces, Fasc. Math., 53, 1-15 (2014).
  • Andrijevic, D.: On the topology generated by preopen sets, Math. Bech., 39, 367-376 (1987).
  • Arenas, F. G., Dontchev J. and Puertas, M L.: Idealization of some weak separation axioms, Acta Math. hungar., 89, 47-53 (2000).
  • Chattopadhyay C. and Roy, U. K.: sets, irresolvable and resolvable space, Math. Solvaca., , 371-378 (1992).
  • Dontchev, J., Ganster, M. and Rose, D.: Ideal reslovalibity, Topology and its Appl., 93, 1-16 (1999).
  • Ekici, E.: On a-open sets, A -sets and decompositions of continuity and supra-continuity, Annales Univ. Sci. Budapest., 51, 39-51 (2008).
  • Ekici, E.: A note on a-open sets and e -open sets, Filomat, 22, 89-96 (2008).
  • Ekici, E.: New forms of contra-continuity, Carpathian J. Math., 24, 37-45 (2008).
  • Ekici, E.: Some generalizations of almost contra-super-continuity, Filomat, 21, 31-44 (2007).
  • Hamlett, T. R. and Jankovic, D.: Ideals in topological spaces and the set operator , Bull. U.M.I., 7, 863-874 (1990).
  • Hewitt, E.: A problem of set theoretic topology, Duke Math. J., 10, 309-333 (1943).
  • Jankovic, D. and Hamlett T. R.: New topologies from old via ideal, Amer. Math. Monthly., , 295-310 (1990).
  • Kuratowski, K.: Topology, Vol. I, New York, Academic Press, 1966.
  • Levine, N.: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, , 36-41 (1963).
  • Mukherjee, M. N., Roy B. and Sen, R.: On extension of topological spaces in terms of ideals, Topology and its Appl., 154, 3167-3172 (2007).
  • Nasef, A. A. and Mahmoud, R. A.: Some applications via fuzzy ideals, chaos Solutions Fractals, 13, 825-831 (2002).
  • Navaneethakrishnan, M. and Paulraj, J.: g-closed sets in ideal topological space, Acta Math. Hungar., 119, 365-371 (2008).
  • Njastad, O.: On some classes of nearly open sets, Paci…c J Math., 15, 961-970 (1965).
  • Stone, M. H.: Application of the theory of boolean rings to genearted topology, Trans. Amer. Math. Soc., 41, 375-381 (1937).
  • Vaidyanathaswamy, R.: The localization theory in set-topology, Proc. Indian Acad. Sci., 20, 61 (1945).
  • Velicko, N. V.: H-closed topological spaces, Amer. Math. Soc. Trans., 78, 103-118 (1968).
  • Current address : Shyamapada Modak: Department of Mathematics, University of Gour Banga P.O. Mokdumpur, Malda - 732103, India
  • E-mail address : spmodak2000@yahoo.co.in
  • Current address : Md. Monirul Islam: Department of Mathematics, University of Gour Banga P.O. Mokdumpur, Malda - 732103, India
  • E-mail address : moni.math007@gmail.com
Year 2017, Volume: 66 Issue: 2, 323 - 331, 01.08.2017
https://doi.org/10.1501/Commua1_0000000822

Abstract

References

  • Al-Omari, W., Noorani, M., Noiri, T. and Al-Omari, A.: The
  • Al-Omari, W., Noorani, M. and Al-Omari, A.: a-local function and its properties in ideal topological spaces, Fasc. Math., 53, 1-15 (2014).
  • Andrijevic, D.: On the topology generated by preopen sets, Math. Bech., 39, 367-376 (1987).
  • Arenas, F. G., Dontchev J. and Puertas, M L.: Idealization of some weak separation axioms, Acta Math. hungar., 89, 47-53 (2000).
  • Chattopadhyay C. and Roy, U. K.: sets, irresolvable and resolvable space, Math. Solvaca., , 371-378 (1992).
  • Dontchev, J., Ganster, M. and Rose, D.: Ideal reslovalibity, Topology and its Appl., 93, 1-16 (1999).
  • Ekici, E.: On a-open sets, A -sets and decompositions of continuity and supra-continuity, Annales Univ. Sci. Budapest., 51, 39-51 (2008).
  • Ekici, E.: A note on a-open sets and e -open sets, Filomat, 22, 89-96 (2008).
  • Ekici, E.: New forms of contra-continuity, Carpathian J. Math., 24, 37-45 (2008).
  • Ekici, E.: Some generalizations of almost contra-super-continuity, Filomat, 21, 31-44 (2007).
  • Hamlett, T. R. and Jankovic, D.: Ideals in topological spaces and the set operator , Bull. U.M.I., 7, 863-874 (1990).
  • Hewitt, E.: A problem of set theoretic topology, Duke Math. J., 10, 309-333 (1943).
  • Jankovic, D. and Hamlett T. R.: New topologies from old via ideal, Amer. Math. Monthly., , 295-310 (1990).
  • Kuratowski, K.: Topology, Vol. I, New York, Academic Press, 1966.
  • Levine, N.: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, , 36-41 (1963).
  • Mukherjee, M. N., Roy B. and Sen, R.: On extension of topological spaces in terms of ideals, Topology and its Appl., 154, 3167-3172 (2007).
  • Nasef, A. A. and Mahmoud, R. A.: Some applications via fuzzy ideals, chaos Solutions Fractals, 13, 825-831 (2002).
  • Navaneethakrishnan, M. and Paulraj, J.: g-closed sets in ideal topological space, Acta Math. Hungar., 119, 365-371 (2008).
  • Njastad, O.: On some classes of nearly open sets, Paci…c J Math., 15, 961-970 (1965).
  • Stone, M. H.: Application of the theory of boolean rings to genearted topology, Trans. Amer. Math. Soc., 41, 375-381 (1937).
  • Vaidyanathaswamy, R.: The localization theory in set-topology, Proc. Indian Acad. Sci., 20, 61 (1945).
  • Velicko, N. V.: H-closed topological spaces, Amer. Math. Soc. Trans., 78, 103-118 (1968).
  • Current address : Shyamapada Modak: Department of Mathematics, University of Gour Banga P.O. Mokdumpur, Malda - 732103, India
  • E-mail address : spmodak2000@yahoo.co.in
  • Current address : Md. Monirul Islam: Department of Mathematics, University of Gour Banga P.O. Mokdumpur, Malda - 732103, India
  • E-mail address : moni.math007@gmail.com
There are 26 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Shyamapada Modak This is me

Monirul Islam Md. This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Modak, S., & Islam Md., M. (2017). More on α-topological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 323-331. https://doi.org/10.1501/Commua1_0000000822
AMA Modak S, Islam Md. M. More on α-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):323-331. doi:10.1501/Commua1_0000000822
Chicago Modak, Shyamapada, and Monirul Islam Md. “More on α-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 323-31. https://doi.org/10.1501/Commua1_0000000822.
EndNote Modak S, Islam Md. M (August 1, 2017) More on α-topological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 323–331.
IEEE S. Modak and M. Islam Md., “More on α-topological spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 323–331, 2017, doi: 10.1501/Commua1_0000000822.
ISNAD Modak, Shyamapada - Islam Md., Monirul. “More on α-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 323-331. https://doi.org/10.1501/Commua1_0000000822.
JAMA Modak S, Islam Md. M. More on α-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:323–331.
MLA Modak, Shyamapada and Monirul Islam Md. “More on α-Topological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 323-31, doi:10.1501/Commua1_0000000822.
Vancouver Modak S, Islam Md. M. More on α-topological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):323-31.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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