Smooth partitions of unity and differentiable good open covers are important technical tools in the realm of smooth manifolds.

Are there analogs of these tools for piecewise linear manifolds?

A *PL good open cover* of a PL-manifold is a locally finite open cover {U_{i}} such that every finite intersection of U_{i} is either empty or PL-isomorphic to R^{n}.

A *PL partition of unity* subordinate to an open cover {U_{i}} of a PL-manifold X
is a family of nonnegative PL-functions f_{i}: X→R such that supp f_{i} is a subset of U_{i}, supp f_{i} form a locally finite family, and the sum of f_{i} is 1.

**Do PL-manifolds admit PL good open covers? Do open covers of PL-manifolds admit subordinate PL partitions of unity?**