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2020•Fundamental Journal of Mathematics and ApplicationsOpen access

Topological Properties of Digital Line

Soheil Jafari, Gnanachandra PRABU, M. Lellis Thivagar

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Abstract

The main purpose of Digital topology is the study of topological properties of discrete objects which are obtained digitizing continuous objects.Digital topology plays a very important role in computer vision, image processing and computer graphics.The ultimate aim of this article is to analyze the behavior of various general topological concepts in the Khalimsky topology.In this article, we provide some results and examples of topology on Z, the set of all integers.Also, we explain the concepts of digital line and digital intervals with illustrative counterexamples.

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What this paper is about

The main purpose of Digital topology is the study of topological properties of discrete objects which are obtained digitizing continuous objects.Digital topology plays a very important role in computer vision, image processing and computer graphics.The ultimate aim of this article is to analyze the behavior of various general topological concepts in the Khalimsky topology.In this article, we provide some results and examples of topology on Z, the set of all integers.Also, we explain the concepts of digital line and digital intervals with illustrative counterexamples.

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Available abstract

The main purpose of Digital topology is the study of topological properties of discrete objects which are obtained digitizing continuous objects.Digital topology plays a very important role in computer vision, image processing and computer graphics.The ultimate aim of this article is to analyze the behavior of various general topological concepts in the Khalimsky topology.In this article, we provide some results and examples of topology on Z, the set of all integers.Also, we explain the concepts of digital line and digital intervals with illustrative counterexamples.

Key concepts: Topology (electrical circuits), Line (geometry), Computer science, Mathematics, Geometry, Combinatorics

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