Research Article
BibTex RIS Cite

On Weakly e*-θ-open Functions and Their Characterizations

Year 2022, , 56 - 65, 30.06.2022
https://doi.org/10.47000/tjmcs.1015626

Abstract

The main aim of this paper is to introduce and study a new class of weakly open functions called weakly e*-θ-open functions via e*-θ-open sets [13], which is a stronger concept than weakly e*-open functions [22]. Moreover, we obtain various characterizations of weakly e*-θ-open functions and investigate some of their fundamental properties. In additon, we investigate not only the relationships of these functions with some othertypes of existing topological functions, but also several basic results related to connectedness, e*θ-connectedness [5] and hyperconnectedness [18].

Supporting Institution

Türk-Alman Üniversitesi Bilimsel Araştırma Projeleri

Project Number

2021BR01

Thanks

This study was supported by Turkish-German University Scientific Research Projects Commission under the grantno: 2021BR01.

References

  • Andrijevic, D., On b-open sets, Mat. Vesnik,48(1996), 59–64.
  • Arya, S. P., Gupta R., Strongly continuous mappings, Kyungpook Math. J.,14(1974), 131–143.
  • Ayhan, B. S., On e∗θ-regular and e*θ-normal spaces, Advances in Topology and its Structures: Foundations, Theory and Application, inreview.
  • Ayhan, B. S., Özkoç ̧ M., On almost contra e*θ-continuous functions, Jordan J. Math. Stat., 11(4)(2018), 383–408.
  • Ayhan, B. S., Özkoç ̧ M., On contra e*θ-continuous functions, Divulgaciones Matematicas, 19(2)(2018), 1–13.
  • Caldas, M., Navalagi, G., On weak forms of preopen and preclosed functions, Archivum Mathematicum, 40(2004), 119–128.
  • Caldas M., Navalagi G., On weak forms of semi-open and semi-closed functions, Missouri J. Math. Sci., 18(3)(2006), 165–178.
  • Caldas, M., Ekici, E., Jafari, S., Latif, M., On weakly BR-open functions and their characterizations in topological spaces, DemonstratioMathematica, 44(1)(2011), 159-168.
  • Ekici, E., On a-open sets, A*-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. E ̈otv ̈os Sect. Math., 51(2008), 39–51.
  • Ekici, E., On e-open sets,DP*-sets and DPE*-sets and decompositions of continuity, Arabian J. Sci. Eng.,33(2A)(2008), 269–282.
  • Ekici, E., New forms of contra-continuity, Carpathian J. Math., 24(1)(2008), 37–45.
  • Ekici, E., On e*-open sets and(D,S)*-sets, Math. Morav., 13(1)(2009), 29–36.
  • Farhan, A. M., Yang, X. S., New types of strongly continuous functions in topological spaces via δ-β-open sets, Eur. J. Pure Appl. Math., 8(2)(2015), 185–200.
  • Jumaili, A. M. F. A., Abed, M. M., Sharqi, F. G. A., Other new types of mappings with strongly closed graphs in topological spaces via e-θ and δ-β-θ-open sets, The 1st Int. Sci. Conf. P. Sci., (2019), 1–10.
  • Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36–41.
  • Levine, N., Strong continuity in topological spaces, Amer. Math. Monthly, 67(1960), 269.
  • Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47–53.
  • Noiri, T., A generalization of closed mappings, Atti. Accad. Naz. Lince Rend. Cl. Sci. Fis. Mat. Natur.,8(1973), 210–214.
  • Noiri, T., Omari, A. A., Noorani, M. S. M., Weak forms of open and closed functions via b-θ open sets, Demonstratio Mathematica, 42(2009), 193–203.
  • Noiri, T., Omari, A. A., Noorani, M. S. M., Weakly b-open functions,Mathematica Balkanica, 23(2009), 1–13.
  • Özkoç ̧, M., Ayhan, B.S., On weakly eR-open functions, J. Linear Topol. Algebra, 5(3)(2016), 145–153.
  • Özkoç ̧, M., Erdem, S., On weakly e∗-open functions and weakly e*-closed functions, J. Linear Topol. Algebra, 9(3)(2020), 201–211.
  • Rose, D. A., On weak openness and almost openness, Internat. J. Math. and Math. Sci., 7(1984), 35–40.
  • Rose, D. A., Jankovic, D. S., Weakly closed functions and Hausdorff spaces, Math. Nachr., 130(1987), 105–110.
  • Singal, M. K., Singal, A. R., Almost continuous mappings, Yokohama Math. J., 16(1968), 63–73.
  • Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375–381.
  • Velicko, N. V., H-closed topological spaces, Amer. Math. Soc. Transl., 78(2)(1968), 103–118.
Year 2022, , 56 - 65, 30.06.2022
https://doi.org/10.47000/tjmcs.1015626

Abstract

Project Number

2021BR01

References

  • Andrijevic, D., On b-open sets, Mat. Vesnik,48(1996), 59–64.
  • Arya, S. P., Gupta R., Strongly continuous mappings, Kyungpook Math. J.,14(1974), 131–143.
  • Ayhan, B. S., On e∗θ-regular and e*θ-normal spaces, Advances in Topology and its Structures: Foundations, Theory and Application, inreview.
  • Ayhan, B. S., Özkoç ̧ M., On almost contra e*θ-continuous functions, Jordan J. Math. Stat., 11(4)(2018), 383–408.
  • Ayhan, B. S., Özkoç ̧ M., On contra e*θ-continuous functions, Divulgaciones Matematicas, 19(2)(2018), 1–13.
  • Caldas, M., Navalagi, G., On weak forms of preopen and preclosed functions, Archivum Mathematicum, 40(2004), 119–128.
  • Caldas M., Navalagi G., On weak forms of semi-open and semi-closed functions, Missouri J. Math. Sci., 18(3)(2006), 165–178.
  • Caldas, M., Ekici, E., Jafari, S., Latif, M., On weakly BR-open functions and their characterizations in topological spaces, DemonstratioMathematica, 44(1)(2011), 159-168.
  • Ekici, E., On a-open sets, A*-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. E ̈otv ̈os Sect. Math., 51(2008), 39–51.
  • Ekici, E., On e-open sets,DP*-sets and DPE*-sets and decompositions of continuity, Arabian J. Sci. Eng.,33(2A)(2008), 269–282.
  • Ekici, E., New forms of contra-continuity, Carpathian J. Math., 24(1)(2008), 37–45.
  • Ekici, E., On e*-open sets and(D,S)*-sets, Math. Morav., 13(1)(2009), 29–36.
  • Farhan, A. M., Yang, X. S., New types of strongly continuous functions in topological spaces via δ-β-open sets, Eur. J. Pure Appl. Math., 8(2)(2015), 185–200.
  • Jumaili, A. M. F. A., Abed, M. M., Sharqi, F. G. A., Other new types of mappings with strongly closed graphs in topological spaces via e-θ and δ-β-θ-open sets, The 1st Int. Sci. Conf. P. Sci., (2019), 1–10.
  • Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36–41.
  • Levine, N., Strong continuity in topological spaces, Amer. Math. Monthly, 67(1960), 269.
  • Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47–53.
  • Noiri, T., A generalization of closed mappings, Atti. Accad. Naz. Lince Rend. Cl. Sci. Fis. Mat. Natur.,8(1973), 210–214.
  • Noiri, T., Omari, A. A., Noorani, M. S. M., Weak forms of open and closed functions via b-θ open sets, Demonstratio Mathematica, 42(2009), 193–203.
  • Noiri, T., Omari, A. A., Noorani, M. S. M., Weakly b-open functions,Mathematica Balkanica, 23(2009), 1–13.
  • Özkoç ̧, M., Ayhan, B.S., On weakly eR-open functions, J. Linear Topol. Algebra, 5(3)(2016), 145–153.
  • Özkoç ̧, M., Erdem, S., On weakly e∗-open functions and weakly e*-closed functions, J. Linear Topol. Algebra, 9(3)(2020), 201–211.
  • Rose, D. A., On weak openness and almost openness, Internat. J. Math. and Math. Sci., 7(1984), 35–40.
  • Rose, D. A., Jankovic, D. S., Weakly closed functions and Hausdorff spaces, Math. Nachr., 130(1987), 105–110.
  • Singal, M. K., Singal, A. R., Almost continuous mappings, Yokohama Math. J., 16(1968), 63–73.
  • Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375–381.
  • Velicko, N. V., H-closed topological spaces, Amer. Math. Soc. Transl., 78(2)(1968), 103–118.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Burcu Sünbül Ayhan 0000-0001-8359-5609

Project Number 2021BR01
Publication Date June 30, 2022
Published in Issue Year 2022

Cite

APA Ayhan, B. S. (2022). On Weakly e*-θ-open Functions and Their Characterizations. Turkish Journal of Mathematics and Computer Science, 14(1), 56-65. https://doi.org/10.47000/tjmcs.1015626
AMA Ayhan BS. On Weakly e*-θ-open Functions and Their Characterizations. TJMCS. June 2022;14(1):56-65. doi:10.47000/tjmcs.1015626
Chicago Ayhan, Burcu Sünbül. “On Weakly E*-θ-Open Functions and Their Characterizations”. Turkish Journal of Mathematics and Computer Science 14, no. 1 (June 2022): 56-65. https://doi.org/10.47000/tjmcs.1015626.
EndNote Ayhan BS (June 1, 2022) On Weakly e*-θ-open Functions and Their Characterizations. Turkish Journal of Mathematics and Computer Science 14 1 56–65.
IEEE B. S. Ayhan, “On Weakly e*-θ-open Functions and Their Characterizations”, TJMCS, vol. 14, no. 1, pp. 56–65, 2022, doi: 10.47000/tjmcs.1015626.
ISNAD Ayhan, Burcu Sünbül. “On Weakly E*-θ-Open Functions and Their Characterizations”. Turkish Journal of Mathematics and Computer Science 14/1 (June 2022), 56-65. https://doi.org/10.47000/tjmcs.1015626.
JAMA Ayhan BS. On Weakly e*-θ-open Functions and Their Characterizations. TJMCS. 2022;14:56–65.
MLA Ayhan, Burcu Sünbül. “On Weakly E*-θ-Open Functions and Their Characterizations”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 1, 2022, pp. 56-65, doi:10.47000/tjmcs.1015626.
Vancouver Ayhan BS. On Weakly e*-θ-open Functions and Their Characterizations. TJMCS. 2022;14(1):56-65.

Cited By