The continuity of the gauge fixing condition $n\cdot\partial n\cdot A=0$ for $SU(2)$ gauge theory on the manifold $R\bigotimes S^{ 1}\bigotimes S^{ 1}\bigotimes S^{ 1}$ is studied here, where $n^{ \mu}$ stands for directional vector along $x_{ i}$-axis($i=1,2,3$). It is proved that the gauge fixing condition is continuous given that gauge potentials are differentiable with continuous derivatives on the manifold $R\bigotimes S^{ 1}\bigotimes S^{ 1}\bigotimes S^{ 1}$ which is compact.
Categories: physics.gen-ph hep-th