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Locally convex spaces $C^{k,l}(U\\times V,E)$ of functions with different degrees of differentiability in the $U$- and $V$-variable were recently studied by H.Alzaareer, who established an exponential law of the form $C^{k,l}(U\\times V,E)\\cong C^k(U,C^l(V,E))$. 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