Research Article
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Year 2019, Volume: 3 Issue: 2, 112 - 128, 30.12.2019

Shyamapada Modak , Md Monirul Islam

https://doi.org/10.29002/asujse.605003

Abstract

References

  • [1] K. Kuratowski, Topology, Vol. I. New York: Academic Press, 1966.
  • [2] R.Vaidyanathswamy, The localisation theory in set topology, Proc. India Acad. Sci., 20 (1945) 51-61.
  • [3] T. R. Hamlett, D.Jankovi , Ideals in Topological Spaces and the Set Operator , Bollettino U. M. I., 7 (4-B) (1990) 863-874.
  • [4] D. Jankovi , T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990) 295-310.
  • [5] P. Samuels, A topology formed from a given topology and ideal, J. Lond. Math. Soc., 10 (1975) 409-416.
  • [6] E. Hayashi, Topologies defined by local properties, Math. Ann., 156 (1964) 205-215.
  • [7] H. Hashimoto, On the *-topology and its application, Fund. Math., 91 (1976) 5-10.
  • [8] R.L. Newcomb, Topologies Which are Compact Modulo an Ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, 1967.
  • [9] S. Modak, Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82 (3) (2012) 233-243.
  • [10] S. Modak, Minimal spaces with a mathematical structure, J. Assoc. Arab Univ. BasicAppl. Sci., 22 (2017) 98-101.
  • [11] C. Bandyopadhyay, S.Modak, A new topology via -operator, Proc. Nat. Acad. Sci.India, 76(A), IV (2006) 317-320.
  • [12] S. Modak, C. Bandyopadhyay, A note on - operator, Bull. Malyas. Math. Sci. Soc., 30 (1) (2007) 43-48.
  • [13] S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat, 29 (4) (2015) 661-665.
  • [14] A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math., 43 (2)(2013) 139-149.
  • [15] A. Al-Omari, T. Noiri, On -operator in ideal -spaces, Bol. Soc. Paran. Mat., (3s.), 30 (1)(2012) 53-66.
  • [16] A. Al-Omari, T. Noiri, On operators in ideal minimal spaces, Mathematica, 58 (81), No. 1-2 (2016) 3-13.
  • [17] W.F. Al-Omeri, Mohd.Salmi, Md.Noorani, T.Noiri, A. Al-Omari, The operator in ideal topological spaces, Creat. Math. Inform., 25 (1) (2016) 1-10.
  • [18] T. Natkaniec, On -continuity and -semicontinuity points, Math. Slovaca, 36 (3) (1986) 297-312.
  • [19] Md. M. Islam, S. Modak, Operator associated with the * and operators, J. Taibah Univ. Sci., 12 (4) (2018) 444-449.
  • [20] S. Modak, Md. M. Islam, On* and operators in topological spaces with ideals, Trans. A. Razmadze Math. Inst., 172 (2018) 491-497.
  • [21] J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], 1999.
  • [22] J. Dontchev, M. Ganster, D. Rose, Ideal resolvability, Topology Appl., 93 (1999) 1-16.
  • [23] D.E. Habil, A.K. Elzenati, Connectedness in isotonic spaces, Turk. J. Math. TUBITAK, 30 (2006) 247-262.
  • [24] B.M.R. Stadler, P.F. Stadler, Higher separation axioms in generalized closure spaces, Comment. Math. Prace Mat., ser.I.-Rocz. Polsk. Tow. Mat., Ser.I., 43 (2003) 257-273.
  • [25] D.E. Habil, A.K. Elzenati, Topological Properties in Isotonic Spaces, IUG Journal of natural studies, 16 (2) (2008) 1-14.
  • [26] B.M.R. Stadler, P.F. Stadler, Basic properties of closure spaces, J. Chem. Inf. Comput. Sci., 42 (2002) 577-590.
  • [27] M.H. Stone, Application of the theory of Boolean rings to general topology, Trans.Amer. Math. Soc., 41 (1937) 375-481.

New Operators in Ideal Topological Spaces and Their Closure Spaces

Year 2019, Volume: 3 Issue: 2, 112 - 128, 30.12.2019

Shyamapada Modak , Md Monirul Islam

https://doi.org/10.29002/asujse.605003

Abstract

In this paper, we introduce two operators associated with ψ* and *ψ operators in ideal topological
spaces and discuss the properties of these operators. We give further
characterizations of Hayashi-Samuel spaces with the help of these two
operators. We also give a brief discussion on homeomorphism of generalized
closure spaces which were induced by these two operators.

Keywords

ideal topological spaces Hayashi-Samuel space isotonic spaces homeomorphism Δ-operator ∇-operator

References

  • [1] K. Kuratowski, Topology, Vol. I. New York: Academic Press, 1966.
  • [2] R.Vaidyanathswamy, The localisation theory in set topology, Proc. India Acad. Sci., 20 (1945) 51-61.
  • [3] T. R. Hamlett, D.Jankovi , Ideals in Topological Spaces and the Set Operator , Bollettino U. M. I., 7 (4-B) (1990) 863-874.
  • [4] D. Jankovi , T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990) 295-310.
  • [5] P. Samuels, A topology formed from a given topology and ideal, J. Lond. Math. Soc., 10 (1975) 409-416.
  • [6] E. Hayashi, Topologies defined by local properties, Math. Ann., 156 (1964) 205-215.
  • [7] H. Hashimoto, On the *-topology and its application, Fund. Math., 91 (1976) 5-10.
  • [8] R.L. Newcomb, Topologies Which are Compact Modulo an Ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, 1967.
  • [9] S. Modak, Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82 (3) (2012) 233-243.
  • [10] S. Modak, Minimal spaces with a mathematical structure, J. Assoc. Arab Univ. BasicAppl. Sci., 22 (2017) 98-101.
  • [11] C. Bandyopadhyay, S.Modak, A new topology via -operator, Proc. Nat. Acad. Sci.India, 76(A), IV (2006) 317-320.
  • [12] S. Modak, C. Bandyopadhyay, A note on - operator, Bull. Malyas. Math. Sci. Soc., 30 (1) (2007) 43-48.
  • [13] S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat, 29 (4) (2015) 661-665.
  • [14] A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math., 43 (2)(2013) 139-149.
  • [15] A. Al-Omari, T. Noiri, On -operator in ideal -spaces, Bol. Soc. Paran. Mat., (3s.), 30 (1)(2012) 53-66.
  • [16] A. Al-Omari, T. Noiri, On operators in ideal minimal spaces, Mathematica, 58 (81), No. 1-2 (2016) 3-13.
  • [17] W.F. Al-Omeri, Mohd.Salmi, Md.Noorani, T.Noiri, A. Al-Omari, The operator in ideal topological spaces, Creat. Math. Inform., 25 (1) (2016) 1-10.
  • [18] T. Natkaniec, On -continuity and -semicontinuity points, Math. Slovaca, 36 (3) (1986) 297-312.
  • [19] Md. M. Islam, S. Modak, Operator associated with the * and operators, J. Taibah Univ. Sci., 12 (4) (2018) 444-449.
  • [20] S. Modak, Md. M. Islam, On* and operators in topological spaces with ideals, Trans. A. Razmadze Math. Inst., 172 (2018) 491-497.
  • [21] J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], 1999.
  • [22] J. Dontchev, M. Ganster, D. Rose, Ideal resolvability, Topology Appl., 93 (1999) 1-16.
  • [23] D.E. Habil, A.K. Elzenati, Connectedness in isotonic spaces, Turk. J. Math. TUBITAK, 30 (2006) 247-262.
  • [24] B.M.R. Stadler, P.F. Stadler, Higher separation axioms in generalized closure spaces, Comment. Math. Prace Mat., ser.I.-Rocz. Polsk. Tow. Mat., Ser.I., 43 (2003) 257-273.
  • [25] D.E. Habil, A.K. Elzenati, Topological Properties in Isotonic Spaces, IUG Journal of natural studies, 16 (2) (2008) 1-14.
  • [26] B.M.R. Stadler, P.F. Stadler, Basic properties of closure spaces, J. Chem. Inf. Comput. Sci., 42 (2002) 577-590.
  • [27] M.H. Stone, Application of the theory of Boolean rings to general topology, Trans.Amer. Math. Soc., 41 (1937) 375-481.
There are 27 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Shyamapada Modak 0000-0002-0226-2392

Md Monirul Islam

Publication Date December 30, 2019
Submission Date August 10, 2019
Acceptance Date December 19, 2019
Published in Issue Year 2019Volume: 3 Issue: 2

Cite

APA Modak, S., & Islam, M. M. (2019). New Operators in Ideal Topological Spaces and Their Closure Spaces. Aksaray University Journal of Science and Engineering, 3(2), 112-128. https://doi.org/10.29002/asujse.605003

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