Triangulations of Subanalytic Sets and Locally Subanalytic Manifolds
Masahiro Shiota, M. Yokoi · Transactions of the American Mathematical Society · 1984
If two polyhedrons are locally subanalytically homeomorphic (that is, the graph is locally subanalytic), they are ${\text {PL}}$ homeomorphic. A locally subanalytic manifold is one whose coordinate transformations are locally subanalytic. It is proved that a locally subanalytic manifold has a unique ${\text {PL}}$ manifold structure. A semialgebraic manifold also is considered.