I just wanted to clear this up, because i think a question I'm attempting may be somewhat badly written. It talks about a set of functions being 'bounded pointwise by 1' - but isn't that just 'bounded by 1'? I don't understand in what sense it is bounded pointwise by a single value, because surely as 1 is constant, it is uniformly bounded by 1? Perhaps the question is just confusingly phrased.
Thanks for the help - M.