It is proved in this note that all Hurwitz Polynomials of order not less than from two simply connected Borel cones in the polynomial parameter space. Based on this result, adge theorems for Huiwitz sta-bility of general polyhedrons of polynomials and boundary theorems for Hurwitz stability of compact sets of and polynomials are obtaned. Both cases of families of polynomials with dependent and independent coefficients are considered. Different from the previous ones, our edge theorems and boundary theorems are applicable to both monic and nonmonic polynomical farnilies and do not require the convexity or the connectivity of the set of polynomials. Moreover, and bouodary theorem for families of polynomials with dependent coefficients does not require the coefficient dependency relation to be affine.