Symbols:Set Theory/Mapping

Mapping
A mapping $f \subset A \times B$ can be written:


 * $f: A \to B$

or:
 * $A \stackrel {f} {\longrightarrow} B$

If $a \in A$ and $b \in B$ such that $\map f a = b$ then we can write:


 * $f: a \mapsto b$

If $f$ is an injection this can be written:


 * $f: A \rightarrowtail B$ or $f: A \hookrightarrow B$

Similarly a surjection can be written:


 * $f: A \twoheadrightarrow B$

Notations for bijection include:


 * $f: A \leftrightarrow B$ or $f: A \stackrel {\sim} {\longrightarrow} B$

The $\LaTeX$ code for these symbols are as follows: