Prove the following statements about continuous functions and
discrete and indiscrete topological spaces: (i) If X is discrete,
then every continous function f from X to any other topological
space Y is continuous. (ii) If X is not discrete, then there is a
topological space Y and a function f: X preimage Y that is not
continuous. ( Hint, Let Y be the set X with the discrete topology
). note: the subject is topology.