It is a reality that general topology is an essential tool for certain aspects of theoretical computer Science.Conversely,the problems that arise in the computational setting have provided new and interesting stimuli for topology.It is also clear that the applications of topology to the area of programming semantics involve also order in an essential way.Domain theory is the area that has combined order and topology for application to theoretical computation most effectively.General topology has many applications in the theory of image processing.One of the important theorems in the theory of computer graphics is the digital Jordan curve theorem,it is proved by using a topological approach.