Question: For sets A and B, define A B = {a b : a A, b B}. (a) Prove that if A and B are open,

For sets A and B, define A B = {a b : a A, b B}. (a) Prove that if A and B are open, then A B is open. (b) Prove that if A and B are compact, then A B is compact. (c) It is not true that the sum of closed sets must be closed. Provide an example to demonstrate this

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