Topologies and all that -- A Tutorial

TL;DR

This tutorial provides an accessible introduction to topology, covering fundamental concepts, constructions, separation properties, metric spaces, and applications in computing, aimed at beginners and practitioners alike.

Contribution

It offers a comprehensive overview of basic topological concepts and their applications, serving as an educational resource for newcomers.

Findings

Clarifies fundamental topological concepts

Explains applications of topology in computing

Provides foundational knowledge for further study

Abstract

This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.