  We develop a tighter implementation of basic PL topology, which keeps track
of some combinatorial structure beyond PL homeomorphism type. With this
technique we clarify some aspects of PL transversality and give combinatorial
proofs of a number of known results.
  New results include a combinatorial characterization of collapsible polyhedra
in terms of constructible posets (generalizing face posets of constructible
simplicial complexes in the sense of Hochster). The relevant constructible
posets are also characterized in terms of Reading's zipping of posets, which is
a variation of edge contractions in simplicial complexes.
