Let $M$ be a compact topological manifold and $C(M)$ the commutative unital $C^*$-algebra of complex valued continuous functions on $M$. Suppose that $M$ admits a piecewise linear structure.
In the introduction of Blackadar and Cuntz's paper it is stated that
a piecewise linear structure on $M$ may be regarded as a suitable choice of generators of $C(M)$.
Question: What makes a choice of generators of $C(M)$ "suitable" so that these generators define a PL structure on $M$? In other words, when exactly does a set of generators of $C(M)$ define a PL structure on $M$?
Any references would be appreciated.