In a proof of the Borsuk-Ulam theorem I've encuntered the notion of a PL mapping between two n-spheres. Does anyone know what it means?
PL stands for "piecewise linear". Roughly, it means a map which can be decomposed as a piecewise linear map with respect to suitable triangulations of source andtarget. For a more precise description, see the wikipedia entry, or these lecture notes of Jacob Lurie. (Note that is probably implicit in the discussion you are reading that the $n$-spheres are given their standard PL structures.)