Topological Spaces

Abstract

A topological space (X,τ) is a set X with a topology τ, i.e., a collection of subsets of X with the following properties:

• 1. X∈τ, ∅∈τ;

• 2. If A,B∈τ, then A∩B∈τ;

• 3. For any collection {A _α } _α , if all A _α ∈τ, then ⋃ _α A _α ∈τ.