In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.