Applications of topology in computer algorithms

TL;DR

This paper explores how general topology can be applied to improve algorithms in modeling, simulation, computer graphics, and image processing, emphasizing the importance of algorithmic development over hardware advances.

Contribution

It highlights specific applications of general topology in computer algorithms, focusing on areas like modeling, simulation, graphics, and image processing.

Findings

Topology informs the development of algorithms in various computer science fields.

Advances in algorithms are crucial for progress in computer graphics and image processing.

Hardware improvements complement but do not replace algorithmic innovations.

Abstract

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorithms. The applications of general topology in other branches of mathematics are not discussed, since they are not applications of mathematics outside of mathematics.