# Thread: Supremum of Continuous functions

1. ## Supremum of Continuous functions

Hi,

I need an example to show that the supremum of continuous functions is a lower semi continuous function (not a continuous function).

Thanks

2. Let $f_{n}(x)=|x|^{1/n}\ \ n\geq 1$

Can you find the piecewise definition of $sup\ f_{n}(x)$?