# Perfect Set in $\mathbb{R}$ with constraint.

Given any uncountable subset $S$ of $\mathbb{R}$ , does there exist a non empty perfect set $A$ such that $A \subseteq S$ ?

• What's a perfect set? – Henrik Jun 3 '17 at 8:48
• I think that $S =\mathbb{R}\setminus \mathbb{Q}$ does not contain any nonempty perfect set. – Rigel Jun 3 '17 at 8:50
• It has...problem in Rudin ...chapter 2 qstn 18 – CoffeeCCD Jun 3 '17 at 8:52
• math.stackexchange.com/questions/1064/… – CoffeeCCD Jun 3 '17 at 9:13
• Oh yes, sorry, you are right! – Rigel Jun 3 '17 at 9:15