# Basic Topology about metric space $R$ [duplicate]

Is there a nonempty perfect set in $R$ which contains no rational number? Its the excercise of Principles of Mathematical Analysis by Walter Rudin. I can't find the answer.I try to construct a set as cantor set but I can't prove it has no rational number or maybe it doesn't exist .Can anyone give me a hint ?I thought abt it for a whole day.
• @B.Mehta Its in$R^2$.I just want to know that in$R^1$.I just began to study mathematical analysis of 1 dimension. – CJWHQ May 11 '18 at 13:27