In this article, we show that the set of Mills constants (real numbers \( M \) such that \( \lfloor M^{3^n} \rfloor \) is prime for all \( n \geq 0 \)) is the increasing limit of sets homeomorphic to the triadic Cantor's set.

More generally, for a given function \( \varphi \) and a set \( A \) of integers, we study the Mills sets \( \mathcal{M}_\varphi(A) = \{\alpha \in \mathbb{R} \,/\, \forall n \in \mathbb{N},\ \lfloor \varphi_n(\alpha) \rfloor \in A\} \) (where \( \varphi_n = \varphi \circ \cdots \circ \varphi \) n times). We show that, under certain assumptions on \( \varphi \) and \( A \), for all real \( w > \inf \mathcal{M}_\varphi(A) \), the set \( \mathcal{M}_\varphi(A) \cap [2, w] \) is homeomorphic to the triadic Cantor's set.