some confusion in lower limit topology?

Question

which of the following function is continious from $R_{l}$ to $R_{l}$ where$R_{l}$ isthe lower limit topology ?

1.f(x) = x

2.f(x) =[x]

3.f(x) = sinx

as option 1 is correct by definition ,,im confused about option 2 and option 3 pleas help me