Definition:Graph of Real Function

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Let $U \subseteq \R^n$ be an open subset of $n$-dimensional Euclidean space.

Let $f : U \to \R^k$ be a real function.

The graph $\map \Gamma f$ of the function $f$ is the subset of $\R^n \times \R^k$ such that:

$\map \Gamma f = \set {\tuple {x, y} \in \R^n \times \R^k: x \in U \subseteq \R^n : \map f x = y}$

where $\times$ denotes the Cartesian product.