A family $\bfam$ of continuous real-valued functions on a space $X$ is said
to be {\sl basic} if every $f \in C(X)$ can be represented $f = \sum_{i=1}^n
g_i \circ \phi_i$ for some $\phi_i \in \bfam$ and $g_i \in C(\R)$ ($i=1, ...,
n$). Define $\basic (X) = \min \{|\bfam| : \bfam$ is a basic family for $X\}$.
If $X$ is separable metrizable $X$ then either $X$ is locally compact and
finite dimensional, and $\basic (X) < \aleph_0$, or $\basic (X) =
\mathfrak{c}$.