General Introduction

Abstract

A topological space is a pair (X,τ) consisting of a set X and a collection τ of subsets of X, called open sets, satisfying the following axioms:

• O₁: The union of open sets is an open set.

• O₂: The finite intersection of open sets is an open set.

• O₃: X and the empty set ∅ are open sets.

The collection τ is called a topology for X. The topological space (X,τ) is sometimes referred to as the space X when it is clear which topology X carries.