A model of π-pre-topological structures and related to human heart

Article type: Research Article

Authors: Osman, H. Saber^{a; *} | El-Sheikh, S.A.^b | Radwan, Abdelaziz E.^a | El-Atik, Abdelfattah A.^{c; 1}

Affiliations: [a] Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt | [b] Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt | [c] Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Correspondence: [*] Corresponding author. H. Saber Osman, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt. E-mail: [email protected].

Note: [1] https://orcid.org/0000-0002-5309-2741

Abstract: In this paper, the generalization of pre-topological spaces called bipretopological spaces (briefly, π-pre-topology) depending on two pre-topologies on an arbitrary universal set has been introduced. New kinds of separations axioms on π-pre-topological spaces are established and some of their properties are investigated. A comparison between four separation axioms on π-pre-topological spaces and pre-topological spaces with different sorts of counterexamples are presented. The topological property for some π-pre-separation axioms are satisfied and its relation with disubgraphs are discussed. A human heart will be studied through it is generated digraph. It is noted that all separation axioms for human heart are not all satisfied.

Keywords: Pre-topology, π-pre-topology, separation axioms, human heart, regularity, normality, hereditary, pre-topological property

DOI: 10.3233/JIFS-223891

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 6, pp. 9431-9439, 2023