# Applying functions to members of members… of lists of lists…, etc

Suppose that I have a list of depth $$k$$, and I want to apply a function $$f$$ to all elements at level $$n$$ - e.g. $$f,\{\{\{a,b\},\{b,c\}\},\{\{c,d\}\}\},3\mapsto\{\{\{f(a),f(b)\},\{f(b),f(c)\}\},\{\{f(c),f(d)\}\}\}$$.

Presumably this can be done with some combination of the built-ins Map, Level, Apply, and Depth, but I can't seem to get it to work. Is there a way to define a function Function[<f>,<list>,<levelspec>] which applies a function only to terms at a certain depth in a list of lists?

Use {n} as the level spec to apply the function only to elements at level n. If you use n as the level spec, the function is applied to elements at levels 1 thru n.
lst = {{{a, b}, {b, c}}, {{c, d}}}