Some nano topological structures via ideals and graphs
El-Atik, A., Hassan, H. (2020). Some nano topological structures via ideals and graphs. EKB Journal Management System, 28(1), 1-21. doi: 10.1186/s42787-020-00093-5
Abd El-Fattah A. El-Atik; Hanan Z. Hassan. "Some nano topological structures via ideals and graphs". EKB Journal Management System, 28, 1, 2020, 1-21. doi: 10.1186/s42787-020-00093-5
El-Atik, A., Hassan, H. (2020). 'Some nano topological structures via ideals and graphs', EKB Journal Management System, 28(1), pp. 1-21. doi: 10.1186/s42787-020-00093-5
El-Atik, A., Hassan, H. Some nano topological structures via ideals and graphs. EKB Journal Management System, 2020; 28(1): 1-21. doi: 10.1186/s42787-020-00093-5

Some nano topological structures via ideals and graphs

Journal of the Egyptian Mathematical Society
Volume 28, Issue 1, June 2020, Page 1-21  XML PDF (2.8 MB)
DOI: 10.1186/s42787-020-00093-5
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Authors
Abd El-Fattah A. El-Atik; Hanan Z. Hassan
Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt
Abstract
In this paper, new forms of nano continuous functions in terms of the notion of
nano Iα-open sets called nano Iα-continuous functions, strongly nano Iα-continuous
functions and nano Iα-irresolute functions will be introduced and studied. We
establish new types of nano Iα-open functions, nano Iα-closed functions and nano
Iα-homeomorphisms. A comparison between these types of functions and other
forms of continuity will be discussed. We prove the isomorphism between simple
graphs via the nano continuity between them. Finally, we apply these topological
results on some models for medicine and physics which will be used to give a
solution for some real-life problems.

Keywords
Ideals; Nano topology; NIα-open sets; NIα-continuous functions; NIαhomeomorphism functions; Directed graphs; Foetal circulation; Electric circuits
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