TITLE: Any reference that explains generated equivalence relation
QUESTION [14 upvotes]: Im looking for a reference that characterizes when an equivalence relation can be generated from a relation and gives a clear explanation of it.

REPLY [2 votes]: No one actually gave a reference so I'll add one.
The book Introduction to topological manifolds by John M. Lee explains this at some length in the appendix A. Also, he gives good examples of generated equivalence relations in Chapter 3, Quotient Spaces.