Let $(X,\|\cdot\|)$ be a Banach space and $A,B,C\subset X$ closed bounded non-empty convex subsets. Let $+$ denote the Minkowski symbol for addition.
Does the $+$ satisfy: $$A+C\subset B+C\implies A\subset B$$
Let $(X,\|\cdot\|)$ be a Banach space and $A,B,C\subset X$ closed bounded non-empty convex subsets. Let $+$ denote the Minkowski symbol for addition.
Does the $+$ satisfy: $$A+C\subset B+C\implies A\subset B$$