Nomographic functions are nowhere dense

Source abstract

A function f f of n n variables is nomographic if it can be represented in the format $$f ( x 1 , … , x n ) = h ( ϕ 1 ( x 1 ) + ⋯ + ϕ n ( x n ) ) f({x_1}, \ldots ,{x_n}) = h({\phi _1}({x_1}) + \cdots + {\phi _n}({x_n}))$$ where the ϕ i {\phi _i} and h h are continuous. Every continuous function of n n variables has a representation as a sum of not more than 2 n + 1 2n + 1 nomographic functions [textbf9]. This paser gives a constructive proof that the nomographic functions form a nowhere dense subset of the space C [ I n ] C[{I^n}] .