## Mapping Diagram of a
Function

$f: RP^1 \rightarrow RP^1$

The mapping diagram of a function is
the set of arrows from elements of $RP^1$ to elements of $RP^1$ .

We consider $RP^1$ to be $S^1$, the circle, so the mapping diagram
is a ruled "surface" with one boundary $S^1$ and the other a
subset of $S^1$.