Let F : X × Y → Z. We say that F is continuous in each variable separately if for each y0 in Y, the map h : X → Z defined by h(x) = F{x × y0) is continuous, and for each x0 in X, ihe map k : Y → Z defined by k(y) = F(x0 × y) is continuous. Show that if F is continuous, then F is continuous in each variable separately.
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