In the process of constructing a proof, I obtain the following set. Let C be the set of continuous and nondecreasing functions defined on $[0,1]$. Let the set $B$ be given as follows:
$ B=\{b_i\in[0,1]: b_i=\sup_{t\in[0,1]}|h_i(t)|,\,h_i \in C\} $
My question is whether the set $B$ is bounded. In particular, si $B$ bounded above? I don't know how to approach this question so any help/suggestion/comment on how to proceed is really appreciated it!