I´ll refering to "continuous" functions $$ f:R \to R $$ with it´s usual topology I've heard that using power series, can be simplified a lot of work to build a certain type of functions, like using the uniform convergence theorem for sequences of continuous functions. For example, I have asked if I can build a function that has local maxima in the rational (need not be using this, but it is the hint) and another in the set $$ \left\{ {\frac{1} {n}} \right\} \cup \left\{ 0 \right\} $$
may be useful to use these techniques?
