I'm trying to check whether this question might be worded wrong, and here it is:
Show that if $A$ is a convex subset of a topological vector space $X$, $u \in A^o$ (the interior of $A$), $v \in \bar{A}$, and $\lambda \in [0,1)$, then $(1- \lambda)u = \lambda v \in A^o$.
Shouldn't it be that then $(1- \lambda)u + \lambda v \in A^o$? Now if this were the case, then I would think that we're essentially showing that $\lambda \bar{A} + (1- \lambda)A^o \subset A^o$, right?
