Topological representations of simplicial complexes and their applications

Topological models can be used to represent complex systems which originate in the real life world. The aim of this paper is to show the equivalence between complexes and finite spaces. Complexes are used to build topological spaces from a set of vertices, edges and faces under constructing a finite number of building blocks. We study a transformation to illustrate the complex networks of the human brain to simplices. Finally, we give a topological model for simplicial complexes. In this case, we represent the brain as a union of simplicial complexes which may be used to give a diagnosis for a brain cancer.