  A continuous selection of polynomial functions is a continuous function whose
domain can be partitioned into finitely many pieces on which the function
coincides with a polynomial. Given a set of finitely many polynomials, we show
that there are only finitely many continuous selections of it and each one is
semi-algebraic. Then, we establish some generic properties regarding the
critical points, defined by the Clarke subdifferential, of these continuous
selections. In particular, given a set of finitely many polynomials with
generic coefficients, we show that the critical points of all continuous
selections of it are finite and the critical values are all different, and we
also derive the coercivity of those continuous selections which are bounded
from below. We point out that some existing results about {\L}ojasiewicz's
inequality and error bounds for the maximum function of some finitely many
polynomials are also valid for all the continuous selections of them.
