With every set X associate the topological spaces D(X) = (X, Td) and I(X) = (X,...

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With every set X associate the topological spaces D(X) = (X, Td) and I(X) = (X, T,) given by X endowed with the discrete topology Ta and with the indiscrete topology T, respectively. (1) Complete D and I to functors Top Set. Set. →Top (2) Is there any natural transformations I⇒ D? Explain. With every set X associate the topological spaces D(X) = (X, Td) and I(X) = (X, T,) given by X endowed with the discrete topology Ta and with the indiscrete topology T, respectively. (1) Complete D and I to functors Top Set. Set. →Top (2) Is there any natural transformations I⇒ D? Explain.

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1 Let Set denote the category of sets with morphisms set theoretic functions and Top denote the cate... View the full answer