New Operators in Ideal Topological Spaces and Their Closure Spaces

Shyamapada Modak; Md Monirul Islam

doi:10.29002/asujse.605003

EN

New Operators in Ideal Topological Spaces and Their Closure Spaces

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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.

Ayrıntılar

Birincil Dil

İngilizce

Konular

-

Bölüm

Araştırma Makalesi

Yazarlar

Shyamapada Modak ^*
0000-0002-0226-2392
India

Md Monirul Islam
India

Yayımlanma Tarihi

30 Aralık 2019

Gönderilme Tarihi

10 Ağustos 2019

Kabul Tarihi

19 Aralık 2019

Yayımlandığı Sayı

Yıl 2019 Cilt: 3 Sayı: 2

DOI

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

IZ

https://izlik.org/JA66BB69UH

Kaynak Göster

RIS / Bibtex

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

AMA

1.Modak S, Islam MM. New Operators in Ideal Topological Spaces and Their Closure Spaces. Aksaray J. Sci. Eng. 2019;3(2):112-128. doi:10.29002/asujse.605003

Chicago

Modak, Shyamapada, ve Md Monirul Islam. 2019. “New Operators in Ideal Topological Spaces and Their Closure Spaces”. Aksaray University Journal of Science and Engineering 3 (2): 112-28. https://doi.org/10.29002/asujse.605003.

EndNote

Modak S, Islam MM (01 Aralık 2019) New Operators in Ideal Topological Spaces and Their Closure Spaces. Aksaray University Journal of Science and Engineering 3 2 112–128.

IEEE

[1]S. Modak ve M. M. Islam, “New Operators in Ideal Topological Spaces and Their Closure Spaces”, Aksaray J. Sci. Eng., c. 3, sy 2, ss. 112–128, Ara. 2019, doi: 10.29002/asujse.605003.

ISNAD

Modak, Shyamapada - Islam, Md Monirul. “New Operators in Ideal Topological Spaces and Their Closure Spaces”. Aksaray University Journal of Science and Engineering 3/2 (01 Aralık 2019): 112-128. https://doi.org/10.29002/asujse.605003.

JAMA

1.Modak S, Islam MM. New Operators in Ideal Topological Spaces and Their Closure Spaces. Aksaray J. Sci. Eng. 2019;3:112–128.

MLA

Modak, Shyamapada, ve Md Monirul Islam. “New Operators in Ideal Topological Spaces and Their Closure Spaces”. Aksaray University Journal of Science and Engineering, c. 3, sy 2, Aralık 2019, ss. 112-28, doi:10.29002/asujse.605003.

Vancouver

1.Shyamapada Modak, Md Monirul Islam. New Operators in Ideal Topological Spaces and Their Closure Spaces. Aksaray J. Sci. Eng. 01 Aralık 2019;3(2):112-28. doi:10.29002/asujse.605003