Weak separation axioms via almost-ID-sets
محورهای موضوعی : General topologyA. A. Nasef 1 , A. M. Elfky 2 , N. Youns 3 , R. Mareay 4
1 - Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
2 - Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
3 - Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
4 - Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
کلید واژه: Ideal topological spaces, almost-I-open set, almost-ID-set,
چکیده مقاله :
The purpose of this paper is to introduce some new classes of almost ideal topological spaces by using the notion of almost-$I$-open sets and study some of their fundamental properties. We study some low separation axioms in almost ideal topological spaces.
[1] M. E. Abd El-Monsef, E. F. Lashien, A. A. Nasef, On I-open sets and I-continous functions, Kyungpook. Math. J. 32 (1) (1992), 21-29.
[2] M. E. Abd El-Monsef, R. A. Mahmoud, A. A. Nasef, Almost I openness and almost I continuity, J. Egypt. Math. Soc. 7 (2) (1994), 191-200.
[3] B. Assaye, M. Alamneh, L.N. Mishra, Y. Mebrat, Dual skew Heyting almost distributive lattices, Appl. Math. Nonlinear. Sci. 4 (1) (2019), 151-162.
[4] S. Goyal, P. Garg, V. N. Mishra, New composition of graphs and their Wiener indices, Appl. Math. Nonlinear. Sci. 4 (1) (2019), 163-168.
[5] D. Jankovic, T. R. Hamlett, Compatible extensions of ideals, Boll. UMI. 7(6-B) (1992), 453-465.
[6] K. Kuratowski, Topologies I, Warszawa, 1933.
[7] K. Kuratowski, Topology, Academic Press, New York, 1966.
[8] L. N. Mishra, On Existence and Behavior of Solutions to Some Nonlinear Integral Equations with Applications, Ph.D. Thesis, National Institute of Technology, Assam, India, 2017.
[9] V. N. Mishra, S. Delen, I. N. Cangul, Algebraic structure of graph operations in terms of degree sequences, Int. J. Anal. Appl. 16 (6) (2018), 809-821.
[10] V. N. Mishra, S. Delen, I. N. Cangul, Degree sequences of join and corona products of graphs, Electronic. J. Math. Anal. Appl. 7 (1) (2019), 5-13.
[11] S. Muthukumaran, B. Anandh, A. Swaminathan, Fuzzy totally somewhat irresolute mappings, Adv. Math. Sci. J. 9 (10) (2020), 7733-7739.
[12] A. A. Nasef, R. Mareay, Ideal and some application of simply open sets, J. Adv. Math. 13 (3) (2017), 7264-7271.
[13] P. L. Powar, V. N. Mishra, S. Bhadauria, Several generalizations of I s ∗ g -continuous functions in ideal topological spaces, Italian J. Pure. Appl. Math. in press.
[14] R. Vaidyanathaswamy, The localisation theory in the set topology, Proc. Indian. Acad. Sci. 20 (1945), 51-61.
