Let $c\in\mathbb{C}^n$ and let $c_\delta \in B(c, \delta),$ the $\delta-$ ball around $c.$ Further let $V^I$ and $V_\delta^I$ denote the set of isolated solutions of the polynomial systems $F(\mathbf{x}) =c$ and $F(\mathbf{x}) =c_\delta$ respectively. Here $F:\mathbf{C}^n \rightarrow \mathbf{C}^n.$ Then is it true that for any $\epsilon >0,$ one can find a small enough $\delta > 0$ so that

1) for each $x^* \in V^I,$ $\exists$ $y^* \in V^I_\delta$ such that $||x^* - y^*||_2 < \epsilon$

2) for each $y^* \in V^I_\delta, \exists$ $x^* \in V^I$ such that $||x^* - y^*||_2 <\epsilon$.