TITLE: What is the difference between a function and a map?
QUESTION [6 upvotes]: Possible Duplicate:
Is there any difference between mapping and function? 

I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are these notions equivalent?

REPLY [2 votes]: In my experience the two have always been interchangeable. Occasionally one is chosen for emphasis. For instance, sometimes one will use the term "function" to refer specifically to a map of sets with no structure, rather than a continuous map of topological spaces or a homomorphisms of some algebraic objects. Alternatively, the term "map" is sometimes reserved for geometric kinds of things (spaces, manifolds, etc.).