## Closure and boundary of a bounded $\Lambda^\infty$-set

Let $\Lambda = (\Lambda_n)_{n \in \NN}$ be a system of collections $\Lambda_n$ of subsets of $\RR^n$ satisfying Axioms $(\Lambda 1)$–$(\Lambda 7)$. The goal of this post is to describe the topological closure and boundary of a bounded $\Lambda^\infty$-set. To fix notations below, let $X \subseteq \RR^n$ be a bounded, basic $\Lambda^\infty$-set. Let $W \subseteq \RR^{k+n+l}$…