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

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.