ABSTRACT
We have encountered some of the ideas of this section in context in earlier parts of the book. Now we make them more formal.
Definition 2.1.1 Let (X,U) be a topological space. We call a collection of sets S = {Sα}α∈A a basis for the topology U if the collection of all unions of elements of S equals U . In other words, if U ∈ U then there exist Sα ∈ S such that ∪αSα = U .
