  Assume that a projective variety is uniformly valuatively stable with respect
to a polarization. We show that the projective variety is uniformly valuatively
stable with respect to any polarization sufficiently close to the original
polarization. The definition of uniformly valuatively stability in this paper
is stronger than that given by Dervan and Legendre in \cite{D-L20}. We also
define the valuative stability for the transcendental K\"ahler classes. Our
openness result can be extended to the K\"ahler cone of projective manifolds.

Algebraic Geometry;Differential Geometry