1. The problem statement, all variables and given/known data An open-n-cell in R^n defined as (a1,b1) x (a2,b2) x ....... (an, bn). Prove that every open n-cell is open. 2. Relevant equations 3. The attempt at a solution I was thinking of using induction. Clearly the base case n=1 is open as (a1,b1) is open in R1. It is a segment. But my problem is trying to picture an open-n-cell. Some hint would be really good.