Topological Properties of The Digital Line

Abstract

The main purpose of Digital topology is the study of topological properties of discreteobjects which are obtained digitizing continuous objects. Digital topology plays a veryimportant role in computer vision, image processing and computer graphics. The ultimateaim of this article is to analyze the behavior of various general topological concepts in theKhalimsky topology. In this article, we provide some results and examples of topology onZ, the set of all integers. Also, we explain the concepts of digital line and digital intervalswith illustrative counterexamples.