(a) Let f1: X →Y1 and f2: X →Y2 be continuous functions. Show that h: X →Y1 ×Y2, defined by h(x)

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Step 1: u000ARecall the definition of continuity for a function. A function u005C( g: A u005Crightarrow B u005C)

(a) Let $f_1: X \rightarrow Y_1$ and $f_2: X \rightarrow Y_2$ be continuous functions. Show that $h: X \rightarrow Y_1 \times Y_2$, defined by $h(x)=\left(f_1(x), f_2(x)\right)$, is continuous as well. (b) Extend the result of (a) to $n$ functions, for $n>2$.