Definition:Sequentially Computable Vector-Valued Function
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Definition
Let $D \subseteq \R^n$ be a subset of real cartesian $n$-space.
Let $f : D \to \R^m$ be a function from $D$ into real cartesian $m$-space.
Suppose:
- $\map f \bsx = \tuple {\map {f_1} \bsx, \map {f_2} \bsx, \dotsc, \map {f_m} \bsx}$
where $f_1, f_2, \dotsc, f_m$ are the component functions of $f$.
Then, $f$ is a sequentially computable vector-valued function if and only if every $f_i$ is a sequentially computable real-valued function.