$\displaystyle f: (R,T_u) \rightarrow (R,T_{cof}) $

defined by

$\displaystyle f(x)=\left\{ \begin {array}{cc} -1 ,& \mbox x\in Q \\ 1 , &\mbox x\in Q^c \end {array}\right.$

is this function continuous, and is this function closed

I found it closed and not continuous

am I right ?

Thanks in advance