Gusev

There are considered piecewise affine maps which are simplicial relative to a complete simplicial complex. Of such maps two kinds are studied: contractions (such that the complete preimage of a point is connected) and crumples (such that the image of a nonsingle-point straight-line segment is nonsingle-point broken line). Discrete criteria (with regard to properties of these maps at simplices of corresponding complexes) for such maps are proved.