Bifurcating a Line: Expressing a Function without Horizontal Bar

[caffeinemachine]

Hello MHB.

Suppose I have a function $f:X\to Y$ which sends $a$ to $b$.

I want to express this as:

Consider a function $\frac{f:X\to Y}{a\xrightarrow{h}b}$.
OR
Consider a function $\frac{f:X\to Y}{f:a\mapsto b}$.
Only thing, I don't want the 'horizontal bar' which separates $f:X\to Y$ from $a\xrightarrow{h}b$ (or $f:a\mapsto b$).

Does anybody know how to do this?

Also, is there a way to write $h$ on top of $\mapsto$ just as I can right $h$ on top of $\rightarrow$?

 

[I like Serena]

Hello MHB.

Suppose I have a function $f:X\to Y$ which sends $a$ to $b$.

I want to express this as:

Consider a function $\frac{f:X\to Y}{a\xrightarrow{h}b}$.
OR
Consider a function $\frac{f:X\to Y}{f:a\mapsto b}$.
Only thing, I don't want the 'horizontal bar' which separates $f:X\to Y$ from $a\xrightarrow{h}b$ (or $f:a\mapsto b$).

Does anybody know how to do this?

Also, is there a way to write $h$ on top of $\mapsto$ just as I can right $h$ on top of $\rightarrow$?

There are various ways to stack symbols on top of each other.
For instance \stackrel:
$$\stackrel{f:X\to Y}{a\xrightarrow{h}b}$$

To put a symbol on top of \mapsto, you can use \overset{f}{\mapsto}.
$${a\overset{f}{\mapsto} b}$$