Geometry of Subanalytic and Semialgebraic Sets

I. Preliminaries.- §1.1. Whitney stratifications.- §1.2. Subanalytic sets and semialgebraic sets.- §1.3. PL topology and C? triangulations.- II. X-Sets.- §11.1. X-sets.- §11.2. Triangulations of X-sets.- §11.3. Triangulations of X functions.- §11.4. Triangulations of semialgebraic and X0 sets and functions.- §11.5. Cr X-manifolds.- §11.6. X-triviality of X-maps.- §11.7. X-singularity theory.- III. Hauptvermutung For Polyhedra.- §III.1. Certain conditions for two polyhedra to be PL homeomorphic.- §III.2. Proofs of Theorems III.1.1 and III.1.2.- IV. Triangulations of X-Maps.- §IV.l. Conditions for X-maps to be triangulable.- §IV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2?.- §IV.3. Local and global X-triangulations and uniqueness.- §IV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13?.- V. D-Sets.- §V.1. Case where any D-set is locally semilinear.- §V.2. Case where there exists a D-set which is not locally semilinear.- List of Notation.