Show [0,1] is not open in ℝ
[0,1] is open if and only if ℝ\[0,1] is closed.
The Attempt at a Solution
ℝ\[0,1] = (-∞,0) U (1,∞), this set is open. Despite the if and only if statement this is enough to say that [0,1] is not open in ℝ.
Is this correct?