Joyal's CatLab General topology

Contents

• Contributors

• References

• Introduction

• Functions between topological spaces

• Categorical view of topology

• Bestiary of topological conditions and properties

• Introduction to sheaves on a topological space

Introduction

Topology is a ‘subfield’ of mathematics which attempts to capture and study the minimal structure of space. General topology seeks to do this through axiomatizing the idea of neighborhoods of a point. The first definition of a topological space seems to be due to Hausdorff in 1914. We will take a short detour and first introduce metric spaces and use it to explain the general axioms for a topological space.