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The continuity of the gauge fixing condition $n\cdot\partial n\cdot A=0$ for$SU(2)$ gauge theory on the manifold $R\bigotimes S^{1}\bigotimesS^{1}\bigotimes S^{1}$ is studied here, where $n^{\mu}$ stands for directionalvector along $x_{i}$-axis($i=1,2,3$). It is proved that the gauge fixingcondition is continuous given that gauge potentials are differentiable withcontinuous derivatives on the manifold $R\bigotimes S^{1}\bigotimesS^{1}\bigotimes S^{1}$ which is compact.

The Continuity of the Gauge Fixing Condition $n\cdot\partial n\cdot A=0$ for $SU(2)$ Gauge Theory