 For any compact subset formula_34, let formula_35 denote all those functions formula_36 such that formula_37 (note that formula_38 depends on both "K" and formula_30 but we will only indicate "K", where in particular, if formula_40 then the domain of "f" is formula_30 rather than "K").Note that if "f" is a real-valued function on "U", then "f" is an element of formula_42 if and only if it is a formula_43 bump function.Distributions on "U" are defined to be the continuous linear functionals on the space formula_44 of test functions on "U" when this space is endowed with a particular topology (called the canonical LF topology).