  In 1986 Paw{\l}ucki and Ple\'sniak introduced the notion of {\sl uniformly
polynomially cuspidal} (UPC) sets and proved that every relatively compact and
fat subanalytic subset of ${\Rz}^n$ satisfies the UPC condition. Herein we
investigate the UPC property of the sections of a relatively compact open
subanalytic set $E\subset{\Rz}^k\times{\Rz}^n$ and we show that two of the
three parameters in the UPC condition can be chosen independently of the
section, while the third one depends generally on the point defining the
section.
