A Topological Approach of a Human Heart via Nano Pre-ideality

Abd El Fattah A. El Atik

Abstract

A technique to construct new neighborhoods for vertices of graphs will be defined. In this paper, the blood circulation of a human body can be classified by nano pre-\emph{I}-open sets which is properly placed between nano openness and nano preopenness regardless the nano topological ideal. Also, we show that the class of nano pre-\emph{I}-open sets is properly placed between the classes of nano \emph{I} -open and nano preopen sets. We give a decomposition of nano \emph{I}-continuity by proving that a function $f:(X,\tau,\emph{I}) \longrightarrow (Y,\sigma)$ is nano \emph{I}-continuous if and only if it is nano pre-\emph{I}-continuous and nano *-\emph{I}-continuous. Finally, we extend the graph of a blood circulation for a human body with respect to ideals.