A Topological Approach of a Human Heart via Nano Pre-ideality: Abd El Fattah A. El Atik - Team, Support (Thai Journal of Mathematics, 2022)
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-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-I-open sets is properly placed between the classes of nano I -open and nano preopen sets. We give a decomposition of nano I-continuity by proving that a function f:(X,τ,I) (Y,σ) is nano I-continuous if and only if it is nano pre-I-continuous and nano *-I-continuous. Finally, we extend the graph of a blood circulation for a human body with respect to ideals.