Index Sets

Definition: Index Sets

Let \(S\) be a set .

We say that a set \(I\) is an index set of \(S\) if there exists a surjection \(f: I \to S\). We call \(f\) an indexing.

Notation

We use \(s_i\) to denote the element in \(s \in S\) such that \(f(i) = s\).