On Topological Spaces Determined By Subset Systems

In this paper,we discuses the topological spaces determined by subset systems Z and introduce the topology operator dz induced by Z.The main results are:(1)the topological spaces determined by the single point subset system and the finite subset system are coincide;(2)for directed subset system,single subset system,finite subset system,power subset system,and chain system,these five classes of subset system satisfy dz(dz(?))=dz(?).