## Hausdorff limits

In order to prove o-minimality for structures generated by Rolle sets, we need another tool from topology: Hausdorff limits (see Section 21 of Kuratowski’s book). Definition For compact sets $A,B \subseteq \RR^n$, the Hausdorff distance $d(S,T)$ is the greater of the two values $\sup\set{d(x,T):\ x \in S}$ and $\sup\set{d(x,S):\ x \in T}$. Note that \$d_n(A,\emptyset)…