\'Etale-open topology and the stable field conjecture

For an arbitrary field $K$ and $K$-variety $V$, we introduce the \'etale-open topology on the set $V(K)$ of $K$-points of $V$. This topology agrees with the Zariski topology, Euclidean topology, valuation topology when $K$ is separably closed, real closed, $p$-adically closed, respectively. The \'etale open topology on $\mathbb{A}^1(K)$ is not discrete if and only if $K$ is large. Topological properties of the \'etale open topology corresponds to algebraic properties of $K$. As an application, we show that a large stable field is separably closed.