Connected regular sublattices of Euclidean space (Q2639885)

In 1957 [Pac. J. Math. 7, 1239-1241 (1957; Zbl 0081.025)], \textit{A. D. Wallace} has proved that a compact connected sublattice of \({\mathbb{R}}^ 2\) is a cyclic chain. The author considers generalizations of Wallace's theorem. The paper contains two theorems. The first of these carries over the result of Wallace to \({\mathbb{R}}^ 3\). The second, the main result, deals with a general situation involving a finite distributive lattice of breadth n and the space \({\mathbb{R}}^{2n}\).