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- Product of sets and supremum 1 answer
I would like to prove that $\sup (A\cdot B)=\sup A \cdot \sup B$, where $A,B$ are sets of positive real numbers. I've already proved $\sup (A+B)=\sup A +\sup B$ and $\sup (c\cdot A)=c\cdot \sup A$$(c\gt 0)$ easily without any problems. However, I'm stuck in the multiplication $A\cdot B$ case.
I need help.
Thanks a lot