Topological closure and Kolchin dimension for generic derivations

Let $\mathfrak C$ carry a topology $\tau$ satisfying suitable conditions, and let $\tau_{\bar \delta}$ be the topology induced by $x\mapsto\operatorname{Jet}(x)$ into $\mathfrak C^\Gamma$ with its product topology. For $X\subseteq\mathfrak C^n$, write $\overline X^{\tau_{\bar \delta}}$ for its $\tau_{\bar \delta}$-closure. Topological-closure conjecture. For every nonempty $L^{\bar \delta}$-definable $X$, the set $\overline X^{\tau_{\bar \delta}}$ is $L^{\bar \delta}$-definable and

$$\mu\bigl(\overline X^{\tau_{\bar \delta}}\setminus X\bigr)<\mu(X).$$

This proposes a definable topological closure whose boundary has strictly smaller leading Kolchin invariant; the topology conditions are deliberately left as “suitable” in the source, and the conjecture remains open.