Homeomorphic Image of Some Kernels

Abstract

Through this paper, we shall study of kernels of a set with the help of ideals and boundaries of these kernels. We also study the convergence of the associated filter in terms of a point which comes from the kernels. We shall also study the homeomorphic images of these kernels.

Keywords

• filter,associated filter,, fontier points,local function,homeomorphism

References

1. [1] K. Kuratowski, Topology, Vol. I, New York, Academic Press, (1966).
2. [2] R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Co., New York, (1960).
3. [3] T. Natkaniec, On -continuity and -semicontinuity points, Mathematica Slovaca., 36(3), (1986), 297-312.
4. [4] A. Al-Omari, H. Al-Saadi, A topology via -local functions in ideal spaces, Mathematica, 60(83), (2018), 103-110.
5. [5] C. Bandhopadhya, S. Modak, A new topology via -operator, Proceedings of the National Academy of Sciences India, 76(A)IV, (2006), 317-320.
6. [6] T. R. Hamlett, D. Janković, Ideals in topological spaces and the set operator , Bollettino dell’Unione Matematica Italiana, 7 (4-B), (1990), 863-874.
7. [7] H. Hashimoto, On the -topology and its applications, Fundamenta Mathematicae, 91, (1976), 5-10.
8. [8] E. Hayashi, Topologies defined by local properties, Mathematische Annalen, 156, (1964), 205-215.

9. [9] D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly, 97,(1990), 295-310.
10. [10] S. Modak, Some new topologies on ideal topological spaces, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 82(3), (2012), 233-243.
11. [11] S. Modak, C. Bandyopadhyay, A note on -operator, Bulletin of the Malaysian Mathematical Sciences Society, 30(1), (2007), 43-48.
12. [12] P. Samuel, A topology formed from a given topology and ideal, London Mathematical Society, 10,(1975), 409-416.
13. [13] Sk. Selim, T. Noiri, S. Modak, Ideals and the associated filters on topological spaces, Eurasian Bulletin of Mathematics, 2(3), (2019), 80-85.
14. [14] N. Bourbaki, General Topology, Chapter 1-4, Springer, 1989.
15. [15] K. D. Joshi, Introduction to General Topology, Wiley, (1983).
16. [16] H. Maki, Generalized -sets and associated closure operator, The special Issue in Commemoration of Prof. Kazusada Ikeda's Retirement, (1986), 139-146.
17. [17] M. Caldas, S. Jafari, On some applications of b-open sets in topological spaces, Kochi Journal of Mathematics, 2, (2007), 11-19.
18. [18] D.Andrijević, Semi-preopen sets, Matematički Vesnik, 38, (1986), 24-32.
19. [19] D. Andrijević, On b-open sets, Matematički Vesnik, 48, (1996), 59-64.
20. [20] M. H. Stone, Applications of the theory of Boolean ring to general topology, Transactions of the American Mathematical Society, 41(3), (1937), 375-481.