Question: For any S, TCR, we define the subsets S.T = {st: se S, te T}, {s+t:se S, te T}. S+T = For each of

For any S, TCR, we define the subsets S.T = {st: se

For any S, TCR, we define the subsets S.T = {st: se S, te T}, {s+t:se S, te T}. S+T = For each of the following assertions, either prove it or provide a coun- terexample. (a) If S is open, then S T is open. (b) if S is open, then S + T is open.

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