Please advise about the most reasonable way to read this statement. My interpretations are below.
The authors do not define the set operation A + B; I assume A + B = $A cup B$.
Their statement “Show that if either A and B is open, then A + B is open” is incorrect unless it should read “both A and B are open.”
Counterexample when only A is open and B is not: Let $A=B_1(O)subset mathbb{R}^2, B=overline{B_1(2)}subsetmathbb{R}^2$. Then there exist points in B which are not interior points of $Acup B$ (e.g. (3,0), a boundary point of B).
