Characterizations of Hayashi-Samuel Spaces via Boundary Points

Year 2019, Volume: 2 Issue: 3, 219 - 226, 30.09.2019

Shyamapada Modak , Sk Selim Md. Monirul Islam

Abstract

Some new closure operators in topological spaces with ideals are a part of this paper. A comparative study of a new type of boundary point, which is defined  with the help of the local function and the boundary points will be discussed through this paper. Characterizations of Hayashi-Samuel spaces are also an object of this paper.

Keywords

Ideal topological space, Hayashi-Samuel, local function, \psi-operator

References

• [1] A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math. 43(2) (2013), 139-149.
• [2] C. Bandhopadhya, S. Modak, A new topology via y-operator, Proc. Nat. Acad. Sci. India. 76(A), IV, (2006), 317-320.
• [3] N. Bourbaki, General Topology, Chapter 1-4, Springer, 1989.
• [4] J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arXIV:math. Gn/9901017v1 [math.GN], 5 Jan 1999.
• [5] E. Ekici, A new collection which contains the topology via ideals, Trans. A. Razmadze Math. Inst. 172 (2018), 372-377.
• [6] E. Ekici, T. Noiri, Properties of I-submaximal ideal topological spaces, Filomat. 24(4) (2010), 87-94.
• [7] E. Ekici, T. Noiri, On subsets and decompositions of continuity in ideal topological spaces, Arab. J. Sci. Eng. 34(1A) (2009), 165-177.
• [8] T. R. Hamlett, D. Jankovi ´ c, Ideals in Topological Spaces and the Set Operator Y , Bollettino U. M. I. 7(4-B) (1990), 863-874.
• [9] H. Hashimoto, On the -topology and its applications, Fund. Math. 91 (1976), 5-10.
• [10] E. Hatir, T. Noiri, On decompositions of continuity via idealzaton, Acta Math. Hungar. 96 (2002), 341-349.
• [11] E. Hayashi, Topologies defined by local properties, Math. Ann. 156 (1964), 205-215.
• [12] Md. M. Islam, S. Modak, Operator associated with the  and Y operators, Journal of Taibah University for Science, 12(4) (2018), 444-449.
• [13] D. Jankovi ´ c, T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly. 97 (1990), 295-310.
• [14] K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
• [15] S. Modak, Minimal spaces with a mathematical structure, J. Assoc. Arab Univ. Basic Appl. Sci. 22 (2017), 98-101.
• [16] S. Modak, Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 82(3) (2012), 233-243. [17] S. Modak, C. Bandyopadhyay, A note on y-operator, Bull. Malays. Math. Sci. Soc. 30(1) (2007), 43-48.
• [18] S. Modak, C. Bandyopadhyaya, Ideals and some nearly open sets, Soochow J. Math. 32(4) (2006), 541-551.
• [19] S. Modak, C. Bandyopadhyay, -topology and generalized open sets, Soochow J. Math. 32(2) (2006), 201-210.
• [20] S. Modak, B. Garai, S. Modak, Remarks on ideal M-space, Anal. Univ. Oradea Fasc. Mat. Tom. XIX(1) (2012), 207-215.
• [21] S. Modak, Md. M. Islam, On  and Y operators in topological spaces with ideals, Trans. A. Razmadze Math. Inst. 172 (2018), 491-497.
• [22] S. Modak, Md. M. Islam, New form of Njastad’s a-set and Levine’s semi-open set, J. Chung. Math. Soc. 30(2) (2017), 165-175.
• [23] S. Modak, Md. M. Islam, More on a-topological space, Commun. Fac. Sci. Univ. Ankara Series A1: Math. and Stat. 66(2) (2017), 323-331.
• [24] S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat. 29(4) (2015), 661-665.
• [25] T. Natkaniec, On I-continuity and I-semicontinuity points, Math. Slovaca. 36(3) (1986), 297-312.
• [26] A. Pavlovi ´ c, Local Function versus Local Closure Function in Ideal Topological Spaces, Filomat. 30(14) (2016), 3725-3731. [27] R. Vaidyanathswamy, Set topology, Chelsea Publishing Co., New York, 1960.
• [28] P. Samuel, A topology formed from a given topology and ideal, J. London Math. Soc. 10 (1975), 409-416.