# Definition:Vertical Section of Function

## Definition

Let $X$ and $Y$ be sets.

Let $f : X \times Y \to \overline \R$ be an extended real-valued function.

Let $x \in X$.

We define the vertical section $f_x$ of $f$ by:

$\map {f_x} y = \map f {x, y}$

for each $y \in Y$.