It is shown that if on a compact space Q any polynomial\(P_N (z) = \sum\nolimits_1^N {\alpha _i } \left( {\begin{array}{*{20}c} {f_{i1} } \\ \vdots \\ {f_{is} } \\ \end{array} } \right),\sum\nolimits_1^N {|\alpha _i |^z > 0} \), in a system of continuous vector functions with real coefficients such that N=n·s and s=2p +1 has at most n−1 zeros, then Q is homeomorphic to a circle or a part of one.