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Year 2020, Volume: 41 Issue: 2, 360 - 368, 25.06.2020

Shyamapada Modak , Sk Selim Md. Monirul Islam

https://doi.org/10.17776/csj.644158
https://izlik.org/JA52RF75ZT

Abstract

References

  • [1] Kuratowski, K., Topology I. Warszawa, 1933.
  • [2] Al-omari, A. and Noiri, T., A topology via -local functions in ideal m-spaces. Questions Answers Gen. Topology, 30 (2012) 105-114.
  • [3] Al-omari, A. and Noiri, T., Local closure functions in ideal topological spaces. Novi Sad J. Math., 12(2) (2013) 139-149.
  • [4] Modak, S., Grill-filter space. J. Indian Math. Soc., 80 (2012) 313-320.
  • [5] Modak, S., Ideal on generalized topological spaces. Sci. Magna, 11(2) (2016) 14-20.
  • [6] Modak, S., Minimal spaces with a mathematical structure. J. Assoc. Arab Univ. Basic Appl. Sci., 22 (2017) 98-101.
  • [7] Modak, S. and Noiri, T., Remarks on locally closed sets. Acta Comment.Univ.Tartu. Math., 22(1) (2018) 57-64.
  • [8] Modak, S. and Islam, Md. M., On * and operators in topological spaces with ideals. Trans. A. Razmadze Math. Inst., 172 (2018) 491-497.
  • [9] Islam, Md. M. and Modak, S., Operator associated with the * and operators. J. Taibah Univ. Sci., 12(4) (2018) 444-449.
  • [10] Islam, Md. M. and Modak, S., Second approximation of local functions in ideal topological spaces. Acta Comment.Univ.Tartu.Math., 22(2) (2018) 245-256.
  • [11] Ekici, E. and Elmali, O., On Decompositions via Generalized Closedness in Ideal Spaces. Filomat, 29(4) (2015) 879-886.
  • [12] Modak, S. and Mistry, S., Ideal on supra topological space. Int. Journal of Math. Analysis, 6(1) (2012) 1-10.
  • [13] Khan, M., and Noiri, T., Semi-local functions in ideal topological spaces. J. Adv. Res. Pure Math., 2(1) (2010) 36-42.
  • [14] Csaszar, A., Modification of generalized topologies via hereditary classes. Acta Math. Hungar., 115(1-2) (2007) 29-36.
  • [15] zbakir, O.B. and Yildirim, E.D., On some closed sets in ideal minimal spaces. Acta Math. Hungar., 125(3) (2009) 227-235.
  • [16] Hayashi, E., Topologies defined by local properties. Math. Ann., 156 (1964) 205-215.
  • [17] Natkaniec, T., On I-continuity and I-semicontinuity points. Math. Slovaca, 36(3) (1986) 297-312.
  • [18] Hamlett, T.R. and Jankovic, D., Ideals in topological spaces and the set operator . Bull. U.M.I., 7(4-B) (1990) 863-874.
  • [19] Modak, S. and Bandyopadhyay, C., A note on - operator. Bull. Malyas. Math. Sci. Soc., 30(1) (2007) 43-48.
  • [20] Csaszar, A., Generalized open sets. Acta Math. Hungar., 75(1-2) (1997) 65-87.
  • [21] Popa V. and Noiri T., On M-continuous functions. Anal. Univ. ``Dunarea de Jos" Galati, Ser. Mat. Fiz. Mec. Teor. Fasc.II, 18(23) (2000) 31-41.
  • [22] Mashhour, A.S., Allam, A.A., Mahmoud, F.S. and Khedr, F.H., On supra topological spaces. Indian J. Pure and Appl. Math., 14(4) (1983) 502-510.
  • [23] Newcomb, R.L., Topologies which are compact modulo an ideal. Ph. D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
  • [24] Njastad, O., Remarks on topologies defined by local properties. Norske Vid-Akad. Oslo (N.S), 8 (1966) 1-16.
  • [25] Pavlovic, A., Local function versus local closure function in ideal topological spaces. Filomat, 30(14) (2016) 3725-3731.
  • [26] Dontchev, J., Ganster M., Rose D., Ideal resolvability. Topology Appl., 93 (1999) 1-16.
  • [27] Dontchev, J., Idealization of Ganster-Reilly decomposition theorems. arXIV, Math. Gn/9901017VI, (1999).
  • [28] Modak, S., Some new topologies on ideal topological spaces. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82(3) (2012) 233-243.
  • [29] Bandyopadhyay, C. and Modak, S., A new topology via - operator. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 76(2006) 17-20.
  • [30] Jankovic, D. and Hamlett, T.R., New topologies from old via ideals.Amer. Math. Monthly, 97(1990) 295-310.
  • [31] Levine, N., Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly, 70 (1963) 36-41.
  • [32] Mashhour, A.S., El-Monsef, M.E.A. and El-Deeb, S.N., On precontinuous and week precontinuous mappings. Proc. Math. Phys. Soc. Egypt., 53 (1982) 47-53.
  • [33] Andrijevic, D., Semi-preopen sets. Math. Vesnik, 38 (1986) 24-32.
  • [34] El-Monsef, M.E.A., El-Deeb, S.N. and Mahmoud, R.A., -open sets and -continuous mappings. Bull. Fac. Sci., Assiut Univ. 12 (1983) 77-90.
  • [35] Andrijevic, D., On b-open sets. Mat. Vesnik., 48 (1996) 59-64.

Common properties and approximations of local function and set operator $\psi$

Year 2020, Volume: 41 Issue: 2, 360 - 368, 25.06.2020

Shyamapada Modak , Sk Selim Md. Monirul Islam

https://doi.org/10.17776/csj.644158
https://izlik.org/JA52RF75ZT

Abstract

Through this paper, we shall obtain common properties of local function and set operator $\psi$   and introduce the approximations of local function and set operator $\psi$.  We also determined expansion of local function and set operator $\psi$ .

Keywords

local function \psi operator compatible ideal codense ideal

References

  • [1] Kuratowski, K., Topology I. Warszawa, 1933.
  • [2] Al-omari, A. and Noiri, T., A topology via -local functions in ideal m-spaces. Questions Answers Gen. Topology, 30 (2012) 105-114.
  • [3] Al-omari, A. and Noiri, T., Local closure functions in ideal topological spaces. Novi Sad J. Math., 12(2) (2013) 139-149.
  • [4] Modak, S., Grill-filter space. J. Indian Math. Soc., 80 (2012) 313-320.
  • [5] Modak, S., Ideal on generalized topological spaces. Sci. Magna, 11(2) (2016) 14-20.
  • [6] Modak, S., Minimal spaces with a mathematical structure. J. Assoc. Arab Univ. Basic Appl. Sci., 22 (2017) 98-101.
  • [7] Modak, S. and Noiri, T., Remarks on locally closed sets. Acta Comment.Univ.Tartu. Math., 22(1) (2018) 57-64.
  • [8] Modak, S. and Islam, Md. M., On * and operators in topological spaces with ideals. Trans. A. Razmadze Math. Inst., 172 (2018) 491-497.
  • [9] Islam, Md. M. and Modak, S., Operator associated with the * and operators. J. Taibah Univ. Sci., 12(4) (2018) 444-449.
  • [10] Islam, Md. M. and Modak, S., Second approximation of local functions in ideal topological spaces. Acta Comment.Univ.Tartu.Math., 22(2) (2018) 245-256.
  • [11] Ekici, E. and Elmali, O., On Decompositions via Generalized Closedness in Ideal Spaces. Filomat, 29(4) (2015) 879-886.
  • [12] Modak, S. and Mistry, S., Ideal on supra topological space. Int. Journal of Math. Analysis, 6(1) (2012) 1-10.
  • [13] Khan, M., and Noiri, T., Semi-local functions in ideal topological spaces. J. Adv. Res. Pure Math., 2(1) (2010) 36-42.
  • [14] Csaszar, A., Modification of generalized topologies via hereditary classes. Acta Math. Hungar., 115(1-2) (2007) 29-36.
  • [15] zbakir, O.B. and Yildirim, E.D., On some closed sets in ideal minimal spaces. Acta Math. Hungar., 125(3) (2009) 227-235.
  • [16] Hayashi, E., Topologies defined by local properties. Math. Ann., 156 (1964) 205-215.
  • [17] Natkaniec, T., On I-continuity and I-semicontinuity points. Math. Slovaca, 36(3) (1986) 297-312.
  • [18] Hamlett, T.R. and Jankovic, D., Ideals in topological spaces and the set operator . Bull. U.M.I., 7(4-B) (1990) 863-874.
  • [19] Modak, S. and Bandyopadhyay, C., A note on - operator. Bull. Malyas. Math. Sci. Soc., 30(1) (2007) 43-48.
  • [20] Csaszar, A., Generalized open sets. Acta Math. Hungar., 75(1-2) (1997) 65-87.
  • [21] Popa V. and Noiri T., On M-continuous functions. Anal. Univ. ``Dunarea de Jos" Galati, Ser. Mat. Fiz. Mec. Teor. Fasc.II, 18(23) (2000) 31-41.
  • [22] Mashhour, A.S., Allam, A.A., Mahmoud, F.S. and Khedr, F.H., On supra topological spaces. Indian J. Pure and Appl. Math., 14(4) (1983) 502-510.
  • [23] Newcomb, R.L., Topologies which are compact modulo an ideal. Ph. D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
  • [24] Njastad, O., Remarks on topologies defined by local properties. Norske Vid-Akad. Oslo (N.S), 8 (1966) 1-16.
  • [25] Pavlovic, A., Local function versus local closure function in ideal topological spaces. Filomat, 30(14) (2016) 3725-3731.
  • [26] Dontchev, J., Ganster M., Rose D., Ideal resolvability. Topology Appl., 93 (1999) 1-16.
  • [27] Dontchev, J., Idealization of Ganster-Reilly decomposition theorems. arXIV, Math. Gn/9901017VI, (1999).
  • [28] Modak, S., Some new topologies on ideal topological spaces. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 82(3) (2012) 233-243.
  • [29] Bandyopadhyay, C. and Modak, S., A new topology via - operator. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 76(2006) 17-20.
  • [30] Jankovic, D. and Hamlett, T.R., New topologies from old via ideals.Amer. Math. Monthly, 97(1990) 295-310.
  • [31] Levine, N., Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly, 70 (1963) 36-41.
  • [32] Mashhour, A.S., El-Monsef, M.E.A. and El-Deeb, S.N., On precontinuous and week precontinuous mappings. Proc. Math. Phys. Soc. Egypt., 53 (1982) 47-53.
  • [33] Andrijevic, D., Semi-preopen sets. Math. Vesnik, 38 (1986) 24-32.
  • [34] El-Monsef, M.E.A., El-Deeb, S.N. and Mahmoud, R.A., -open sets and -continuous mappings. Bull. Fac. Sci., Assiut Univ. 12 (1983) 77-90.
  • [35] Andrijevic, D., On b-open sets. Mat. Vesnik., 48 (1996) 59-64.
There are 35 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Shyamapada Modak 0000-0002-0226-2392

Sk Selim 0000-0002-4226-2004

Md. Monirul Islam 0000-0003-4748-4690

Submission Date November 8, 2019
Acceptance Date April 1, 2020
Publication Date June 25, 2020
DOI https://doi.org/10.17776/csj.644158
IZ https://izlik.org/JA52RF75ZT
Published in Issue Year 2020 Volume: 41 Issue: 2

Cite

APA Modak, S., Selim, S., & Islam, M. M. (2020). Common properties and approximations of local function and set operator $\psi$. Cumhuriyet Science Journal, 41(2), 360-368. https://doi.org/10.17776/csj.644158

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